# topological

share## Examples

topological's examples

- The "objects" of topology are often formally defined as
**topological**spaces. A set for which a topology has been specified is called a**topological**space (Munkres 2000, p. 76). —*“Topology -- from Wolfram MathWorld”*, - In mathematics, a
**topological**space is an ordered pair where is a set and is a certain collection of subsets of called the open sets or the topology of. A**topological**space is an ordered pair where is a set and is a collection of subsets of (i.e., any element is. —*“Topological space - encyclopedia article - Citizendium”*, - Definition of
**topological**in the Online Dictionary. Meaning of topological. Pronunciation of topological. Translations of topological.**topological**synonyms,**topological**antonyms. Information about**topological**in the free online English. —*“topological - definition of*,**topological**by the Free Online” **topological**(not comparable) (mathematics) of or relating to topology [edit] Derived**topological**space [edit] Translations. of or relating to topology. —*“topological - Wiktionary”*,- (3) G-automorphic, if X is a
**topological**group and each translation systematically appear in many trends of**Topological**Algebra and**Topological**Dy. —*“TOPOLOGICAL TRANSFORMATION GROUPS: SELECTED TOPICS”*, u.cs.biu.ac.il - Ideas that are now classified as
**topological**were expressed as early as 1736. In 1914, Felix Hausdorff coined the term "topological space" and gave the definition for what is now called a Hausdorff space.[6] In current usage, a**topological**space is a slight generalization of Hausdorff. —*“Topology - Wikipedia, the free encyclopedia”*, - We show how this can be used to extend (co)homology. theories to
**topological**stacks. The category of**topological**stacks accommodates various classes of objects si. —*“HOMOTOPY TYPES OF*, math.fsu.edu**TOPOLOGICAL**STACKS” - In mathematics, topology is a branch concerned with the study of
**topological**spaces. Topology is also concerned with the study of the so-called**topological**properties of figures, that is to say properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms). —*“Topology - Wikinfo”*, - a
**topological**space may be restated as follows: A family of subsets T ) be a**topological**space and let A X. A point x in X is. a limit point of A if every. —*“Chapter 3*, education.uncc.edu**Topological**Spaces” - Likewise, the concept of a
**topological**space is concerned with generalizing the structure of sets in Euclidean spaces. In fact, there are many equivalent ways to define what we will call a**topological**space just by defining families of subsets of a given set. —*“Topology/Topological Spaces - Wikibooks, collection of open”*, **topological**groups ( ¦täpə¦läjəkəl ′grüps ) ( mathematics ) Groups which also have a topology with the property that the group operation. —*“Topological group: Definition from ”*,- Entirely ***ogously, one can define
**topological**left and right vector spaces over a (not necessarily commutative)**topological**division ring. Two**topological**vector spaces and over the same**topological**field are said to be. —*“Springer Online Reference Works”*, - We deﬁne the action of a locally compact group G on a
**topological**of a**topological**graph E by a. locally compact group G via a cocycle c : E. 1. G. If G is. —*“Group actions on*, wolfweb.unr.edu**topological**graphs” - Buy topological, Books items on eBay. Find great deals on Business Industrial, Collectibles items and get what you want now!. —
*“topological items - Get great deals on Books, Business”*, **Topological**definition, the study of those properties of geometric forms that remain invariant under certain transformations, as bending or stretching. See more. —*“Topological | Define*,**Topological**at ”- We study (countably) compact and (absolutely) -closed primitive
**topological**inverse semigroups. We describe the structure of compact and countably compact primitive**topological**inverse semigroups and show that any countably compact primitive. —*“Brandt Extensions and Primitive*,**Topological**Inverse Semigroups” **Topological**spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity. They appear in all branches of modern mathematics and can be seen as a central unifying notion. Formally, a**topological**space is a set X together with a collection T. —*“Encyclopedia4U -*, encyclopedia4**Topological**space - Encyclopedia Article”**Topological**Data ***ysis. The title is about a recent mathematical method to ***yze. data**Topological**Data ***ysis. The title is about a recent mathematical method to ***yze. data. —*“Topological Data ***ysis”*, piedmont.edu- Figure 1:
**Topological**entropy generated in a so-called horseshoe: the rectangle is stretched, bent upward and placed over itself. The number of orbits distinguishable in steps grows as , generating the**topological**entropy. —*“Topological entropy - Scholarpedia”*, - X and Y is again a
**topological**stack if Y admits a groupoid presentation [Y X and Y be**topological**stacks. The purpose of these notes is to show. —*“MAPPING STACKS OF*,**TOPOLOGICAL**STACKS”

## Videos

related videos for topological

**Topological Compilation**includes 3 topological figures, the mug-to-torus and an inside-out torus**topological study**using animation techniques to discover architectural expressions.**Preserving Topology and Elasticity for Embedded Deformable Models - SIGGRAPH'09**Project webpage: www.cs.mcgill.ca In this paper we introduce a new approach for the embedding of linear elastic deformable models. Our technique results in significant improvements in the efficient physically based simulation of highly detailed objects. First, our embedding takes into account topological details, that is, disconnected parts that fall into the same coarse element are simulated independently. Second, we account for the varying material properties by computing stiffness and interpolation functions for coarse elements which accurately approximate the behavior of the embedded material. Finally, we also take into account empty space in the coarse embeddings, which provides a better simulation of the boundary. The result is a straightforward approach to simulating complex deformable models with the ease and speed associated with a coarse regular embedding, and with a quality of detail that would only be possible at much finer resolution.**sanji x zoro doujinshi black topological space**-own nothing-**Enhanced topological skeletons of 3D meshes**...**Coffee Cup Donut**To a topologist, a coffee cup and a donut are the same thing.**Holons, Singularity and Topology**Holons are wholes composed of hierarchic parts. The holon has a "self-assertiveness tendency" (wholeness) as well as an "integrative tendency"(part) .This duality is similar to the particle/wave duality of light. (Koestler, 1967). It's a interesting theory but how is that physically or energetically possible? In this movie a engineering concept is given how a single non-breakable membrane can create such holons, which are multi-layered topological spaces. This happens with a penetration process, called a pelastration. Holons are then sub-sets (entanglements, knotting) of the total membrane, and each type will have its unique structure and frequencies. They are like bells with a clapper and a cup. In topological holons a part of the neutral dynamic energy of the membrane is converted - locally - in specific "retarded" energy, which is structured in two parts ( which make a union of two parts but will act as a unity ). More on www.mu6.com**Black Topological Space [Part 3] - Sanji x Zoro**I'm so sorry let ya waiting so long *____* Now, here is the last part of BTS. All Credits you can see at the end. Special Thanks to**Topology: An Introduction**I give an introduction to what topology is all about, and also give an example of an open and a closed set in the real line**3D Printed Topological Model**Here we have a topological model designed by Steven Tippett from Texas. Steve designed this model using topological mesh modeling software and contacted me via my website www.printo3 to 3D print this model for him. I HAVE full permission from Steven to share his model for the world to see! Steven's work can be seen here**Topology #24 Sequential Continuity**Sequentially continuous functions between topological spaces**Braid Topological Math Puzzle**A twisted piece of plastic bag that looks cool. But, hey, no cutting, no tape allowed. Can you do it? Have fun!**PFW 2 - Topology Class**pfw**ZBrush 4 - Move Topological Brush**Move parts of the surface of your mesh independently even if they are close together using the Move Topological Brush in ZBrush 4**Topology #10 Topology Examples**Examples of Topological Spaces**Black Topological Space [Part 1] - Sanji x Zoro**Found it at Hope ya like it ^^ ♥**Through one hole or two?**A topological magic trick**Kabbalah explained in Topological way**When we speak about Kabbalah we think of the Tree of Life. However the Tree is about the "manifested" Universe. The manifested world is - in Kabbalistic view - based on three voids (unmanifested) which come from The Absolute. The 3 voids (layers) are called Ain, Ain Soph and Ain Soph Aur. Laureyssens shows in this video how the Absolute can create these 3 voids, where in this first holon 22 sub-holons (sub-sets) can be created on each of it's voids and/or between the voids. Where each sub-holon will have it's specific vibration(s) depending of it's unique structure. That's like the 22 letters is the Hebrew alphabet. And in each of these 22 holons (letters, universes, frames of reference, ...) again 22 more complex sub-combinations can be made after five (Catalan) steps of combinations. By adding more and more layers - thus by having more complex holons - mass (weight) is increasing and parts of universal energy is locally stored. More complex holons - above a measuring threshold will be called "Matter", below that threshold it will be considered "Energy". This topologic approach is in the line of geometrical thinking of Riemann, Clifford and Einstein, but now - for the first time - explains how the emanation over the paths can happen, since the membrane is the mediator and because all holons and sub-holons are still membrane. In religious terms: God is everywhere and we are part of God.**Black Topological Space [Part 2] - Sanji x Zoro**Here is the second part from BTS ^^ Special thanks to where i found this doujin. Hope ya like this, too Don't forget rate and comment ♥**Topology #7 Continuity of Functions Between Metric Spaces (Part 2)**Alternate definition of continuity between metric spaces.**Topological Insulators and Super Conductors**(September 10, 2009) Stanford Professor Shoucheng Zhang, discusses a new class of topological states that have been experimentally realized. These topological insulators have an insulating gap in the bulk, but have topologically protected edge or surface states due to time reversal symmetry. Stanford University: www.stanford.edu Stanford University Channel on YouTube:**Topology #25 Sequential Continuity Counterexample**A sequentially continuous noncontinuous function with a non first countable domain**Kabbalah, the Tree of Life topologically explained**The central picture in Kabbalah is the Tree of Life containing 10 sefirot and 22 paths. This design was derived from concentric circles (The Bahir). The concept of the tree is to represent how universal energy (Kether) transforms into the World (Malkuth). The Tree is about the "manifested" Universe. which is in Kabbalistic view - based on three voids (unmanifested) which come from The Absolute. The 3 voids are called Ain, Ain Soph and Ain Soph Aur. Laureyssens shows in this video - in an engineering approach - how the Absolute (One) can self-create these 3 first voids by a type of universal coupling action of a Singularity (a non-breakable dynamic spherical Membrane), similar to Ouroboros, the snake that bite it's own tail. The action is a penetration, called a pelastration, that creates from parts of the 2D-surface locally a multi-layered (structured) 3D topological sub-set, called a holon. The holon is a local UNION of two membrane tubes, but acts like a UNIT, where it's three joined M-layers interact and exchange energies. Ain, Ain Soph and Ain Soph Aur are these M-layers in each of the four type of Kabbalistic worlds. The Tree can be seen as a union of dynamic multilayered tubes which start from one or more of the Ain-layers, and where these tubes - by progressing - receive more and more layers. The penetration through the Ain Soph layer by the three superior sefirot (together one three-layered tube) gives an extra cover over this tube with is then called Daath (the ...**topological_sort-2****Topology, non-local geometry and dynamics of coherent structures in wall-bounded flows**This video presentation summarizes the research carried out during the 2010 Summer Program at the Center for Turbulence Research (CTR), NASA/Stanford University, by the group formed by Julio Soria, Callum Atkinson and Xiaohua Wu as visitor researchers and Sergei Chumakov and Iván Bermejo-Moreno as CTR hosts.**The weak star topology and the Banach-Alaoglu theorem**This is a lecture from Dr Feinstein's 4th-year module G14FUN Functional ***ysis. See also Dr Feinstein's blog at and, in particular, the Functional ***ysis screencasts blog page at wp.me In this screencast, Dr Feinstein introduces the weak topology on a normed space and the weak star topology on the dual space. He then proves the Banach-Alaoglu theorem, that the closed unit ball of the dual space is weak star compact. This material is suitable for those with a basic knowledge of normed spaces and their duals, and of infinite products of topological spaces, including Tychonoff's theorem on arbitrary products of compact topological spaces.**Topology Preview**stay tuned for the video**QG-TQFT blues**Quantum Gravity Topological Quantum Field Theory Blues. Mathematician comes to grip with ignorance.**Topology #12 Continuity of Functions Between Topological Spaces**Continuity of functions between Topological Spaces, continuity of constant functions, composition of continuous functions**Hitler Learns Topology**Hitler gets confused about the topological definitions of open and closed sets. Then he totally freaks out.**Time reversal symmetry in a magnetically doped topological insulator**Movie from Supporting Online Material for the paper "Massive Dirac Fermion on the Surface of a Magnetically Doped Topological Insulator," by YL Chen, J.-H. Chu, JG ***ytis, ZK Liu, K. Igarashi, H.-H. Kuo, XL Qi, SK Mo, RG Moore, DH Lu, M. Hashimoto, T. Sasagawa, SC Zhang, IR Fisher, Z. Hussain, and ZX Shen. Published 6 August 2010, Science 329, 659 (2010) Abstract: The movie illustrates the evolution of the constant energy contours of the band structure of undoped Bi2Se3 from binding energy Eb=0.7eV to Fermi-energy (EF). In this energy region, the band staructure evolve from the bulk valence band (BVB) to surface state band (SSB) (through the Dirac point), then to the region where the SSB and bulk conduction band (BCB) coexist.**Topology #9 Topological Spaces**Definition of a Topology and a Topological Space**Physics-Inspired Topology Changes for Thin Fluid Features**SIGGRAPH 2010 paper: Physics-Inspired Topology Changes for Thin Fluid Features Chris Wojtan, Nils Thürey, Markus Gross, and Greg Turk Abstract: We propose a mesh-based surface tracking method for fluid animation that both preserves fine surface details and robustly adjusts the topology of the surface in the presence of arbitrarily thin features like sheets and strands. We replace traditional re-sampling methods with a convex hull method for connecting surface features during topological changes. This technique permits arbitrarily thin fluid features with minimal re-sampling errors by reusing points from the original surface. We further reduce re-sampling artifacts with a subdivision-based mesh-stitching algorithm, and we use a higher order interpolating subdivision scheme to determine the location of any newly-created vertices. The resulting algorithm efficiently produces detailed fluid surfaces with arbitrarily thin features while maintaining a consistent topology with the underlying fluid simulation. Paper PDF: www.cc.gatech.edu**Topological Media, 2003**Sha Xin Wei's Topological Media Lab creates artistic audio-visual experiences based on audience movement. This video describes how we enhanced the Berkeley Motes platform with force sensors and integrated the data into MAX/MSP/Jitter. More information can be found at:**Braid Topological Math Puzzle solution**Here's the way you do it! I hope you liked it! The Korean candies I'm talking about are called taraegwa (타래과) or maejakgwa (매작과), but the way they are folded is actually much simpler than what I do in this video: Here is more about them: .**Lec 33 | MIT 18.02 Multivariable Calculus, Fall 2007**Lecture 33: Topological considerations; Maxwell's equations. View the complete course at: ocw.mit.edu License: Creative Commons BY-NC-SA More information at ocw.mit.edu More courses at ocw.mit.edu**Topology #16 Bases**Bases for a Topology**Character Motion Synthesis by Topology Coordinates (Eurographics 2009)**In this paper, we propose a new method to efficiently synthesize character motions that involve close contacts such as wearing a T-shirt, passing the arms through the strings of a knapsack, or piggy-back carrying an injured person. We introduce the concept of topology coordinates, in which the topological relationships of the segments are embedded into the attributes. As a result, the computation for collision avoidance can be greatly reduced for complex motions that require tangling the segments of the body. Our method can be combinedly used with other prevalent frame-based optimization techniques such as inverse kinematics.**Topology #6 Continuity of Functions Between Metric Spaces (Part 1)**Continuity of Functions Between Metric Spaces**Topology #14 Closed Sets**Closed sets in a topological space**Topological Coverage of Unknown Environment by a Mobile Robot**In applications such as vacuuming, cleaning and demining, a robot must cover an unknown surface. The robot accomplishes coverage of an unknown surface by visiting all reachable surfaces in the environment. The efficiency and completeness of coverage is improved by the construction of a topological map while the robot covers the surface. The topological map is a spatial representation of the environment constructed with information gathered by the robots sensors. Robot uses the constructed topological map to plan complete coverage paths. Existing methods generally use grid maps, which are susceptible to odometry error, inaccuracies in sensors and may require considerable memory and computation. Topological map is based on topological relationships between landmarks. Landmarks are represented by corners because they are naturally ocurring features of the environment. It is rather difficult to store information about what area the robot has covered. This difficulty in storing coverage information is overcome by embedding a cell decomposition within the map. Decomposition method uses the landmarks in the topological map as its cell boundaries. The cells are ideally suited to coverage by a simple zigzag path. Covering the envrionment robot detects new uncovered cells and updates the topological map. Robot moves from one cell to another until all surfaces are covered.**Non-homeomorphic Topological Spaces**This clip shows two non homeomorphic topological spaces (a line segment and a circle). Proof: We have to show that there is no bi-continuos map from the line segment to the circle. If there was such a map we could remove a point of the line segment and the image of this point on the circle. The remaining pieces would then still be homeomorphic. On the other hand the first one has two components while the second one is still connected. Since connectedness is preserved by bi-continous maps we obtain a contradiction. Therefore a bi-continous map from the line to the circle can not exist. qed This Video was produces for a topology seminar at the Leibniz Universitaet Hannover. www-ifm.math.uni-

## Blogs & Forum

blogs and forums about topological

*“With more than 700 member companies in 75 countries, TM Forum is the world's leading industry association focused on improving business effectiveness for service providers and their suppliers. Serving the information, communications and”**— Multipoint***Topological**Links in MTNM rel 3.5 - TM Forum,*“The best theoretical physics blog that the search engine can offer you, by a Czech conservative string theorist, focusing on high-energy physics and the climate change facts”**— The Reference Frame:***Topological**blog,*“/blog. neocartography + information visualization. the notebook of cartographer Zachary Forest Johnson. Feb 21 2009. E00Parser, an ActionScript 3 parser for the Arc/Info Export***topological**GIS format of the "four corners" states) are repeated. There are**topological**GIS formats, like Arc”*— /blog " E00Parser, an ActionScript 3 parser for,**“Robust***topological**sorting and Tarjan's algorithm in Python. home | blog. The Strongly time we can create a**topological**sorting algorithm that does the best”*— Robust***topological**sorting and Tarjan's algorithm in Python,*“Topological trickery. This is a fairly old trick, but still a good one. Publisher Blog. New Scientist. New Scientist. Blog - Short Sharp Science”**— New Scientist Technology Blog:***Topological**trickery - New,*“Blog. Top tip***topological**insulators are hot this year. Zhang (left) next to Molenkamp. By Hamish Johnston in There was a slight panic here in the press room over lunch when we all realized that we will soon be writing about**topological**insulators”*— Top tip...topological insulators are hot this year (Blog,**“Topological Musings November 28, 2007 in Uncategorized | Tags: blog, Exposition, math, problem | by Vishal Lama | Leave a comment. I became interested in mathematical blogging after visiting Terence Tao's and Timothy Gower's blogs on numerous”**— blog " Todd and Vishal's blog,**“A forum to discuss TI topics Unanswered posts in***Topological**Insulators. Return to**Topological**Insulators. The following conversations have been posted, but have not yet received”*—***Topological**Insulators — SCIES-Oxon,*“I have never thought of myself as susceptible to patriotism, but for the second time this year, I've felt proud to be an American. The first incident of”**— Pride: Golden Lion Awarded to Bruce Nauman's "Topological, blog.art21.org*

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