Not a homeomorphism Here an operation on a rectangle is shown that is not a homeomorphism. Punching a hole in a topological space is not bi-continuous. After the hole is made the further change is a homeomorphism. The burning endges symbolize that the topological space depicted does not have an edge around the hole. This Video was produces for a topology seminar at the Leibniz Universitaet Hannover. www-ifm.math.uni-
AlgTop1a: One-dimensional objects This is the first video of the first lecture of this beginner's course in Algebraic Topology. Here we begin to introduce basic one dimensional objects, namely the line and the circle. However each can appear in rather a remarkable variety of different ways.
AlgTop12e: Duality for polygons and the Fundamental Theorem of Algebra (last) We define the dual of a polygon in the plane with respect to a fixed origin and unit circle. This duality is related to the notion of the dual of a cone. Then we give a purely rational formulation of the Fundamental Theorem of Algebra, and a proof which keeps track of the winding number of the image of concentric circles about the origin. This is an argument every undergraduate math student ought to know! This is the fifth and final video of the 12th lecture in this beginner's course in Algebraic Topology, given by Assoc Prof NJ Wildberger at UNSW.
Coffee Mug to Donut The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. A topologist is a mathematician who can't tell the difference between a coffee mug and a donut-both are surfaces of genus 1. This Demonstration shows a continuous deformation-known as a homeomorphism-of a coffee mug into a donut, then back to a coffee mug. Contributed by: SM Blinder
AlgTop0: Introduction to Algebraic Topology This is the Introductory lecture to a beginner's course in Algebraic Topology given by NJ Wildberger of the School of Mathematics and Statistics at UNSW in 2010. This first lecture introduces some of the topics of the course and three problems.
Swan Homeomorphisms Two object are called homeomorphic if they can be bi-continuosly deformed into each other. Here two swans are defromed together with their mirrorimages. The result is a torus for one swan and the union of two tori for the other. It is a deep topological theorem that these two can not be bi-continuously deformed into each other. Remark: The by-continuous deformation in this clip only starts after the one swan has put its beak under its feathers. Touching parts of a space that did not touch is NOT a bi-continuous deformation. This video was produced for a topology course at the Leibniz Universitat Hannover.
AlgTop2: Homeomorphism and the group structure on a circle This is the first video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic. Then we introduce the group structure on a circle, or in fact a general conic, in a novel way, following Lemmermeyer and as explained by S. Shirali. This gives a gentle intro to the definition of a group. It also uses Pascal's theorem in an interesting way, so we give some background on projective geometry. This lecture is part of a beginner's course in Algebraic Topology given by NJ Wildberger at UNSW.
AlgTop2a: Homeomorphism and the group structure on a circle This is the first video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic. Then we introduce the group structure on a circle, or in fact a general conic, in a novel way. This gives a gentle intro to the definition of a group. It also uses Pascal's theorem in an interesting way, so we give some background on projective geometry.
AlgTop2b: Homeomorphism and the group structure on a circle (cont.) This is the second video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic. Then we introduce the group structure on a circle, or in fact a general conic, in a novel way. This gives a gentle intro to the definition of a group. It also uses Pascal's theorem in an interesting way, so we give some background on projective geometry.
AlgTop2d: Homeomorphism and the group structure on a circle (cont.) This is the fourth video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic. Then we introduce the group structure on a circle, or in fact a general conic, in a novel way. This gives a gentle intro to the definition of a group. It also uses Pascal's theorem in an interesting way, so we give some background on projective geometry.
AlgTop2f: Homeomorphism and the group structure on a circle (last) This is the sixth and final video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic. Then we introduce the group structure on a circle, or in fact a general conic, in a novel way. This gives a gentle intro to the definition of a group. It also uses Pascal's theorem in an interesting way, so we give some background on projective geometry.
AlgTop23: Knots and surfaces II In the 1930's H. Siefert showed that any knot can be viewed as the boundary of an orientable surface with boundary, and gave a relatively simple procedure for explicitly constructing such `Seifert surfaces'. We show the algorithm, exhibit it for the trefoil and the square knot, and then discuss Euler numbers for surfaces with boundaries. This is part of a beginner's course on Algebraic Topology given by NJ Wildberger of the School of Mathematics and Statistics, UNSW.
Homeomorphism, LMMS dubstep Just started using LMMS - thought I'd take a shot at some electronic music for a change.
Coffee Cup Donut To a topologist, a coffee cup and a donut are the same thing.
Aditya Mittal on Topological Representations of Circle This video shows several different ways of representing a circle and what it is to be homeomorphic to a circle. It tries to help build a very conceptual understanding of the topological concept without all the formalism and equations. I make no claim to having made any of these concepts. I am only reiterating in an easy to understand and concise manner.
AlgTop14: The Ham Sandwich theorem and the continuum In this video we give the Borsuk Ulam theorem: a continuous map from the sphere to the plane takes equal values for some pair of antipodal points. This is then used to prove the Ham Sandwich theorem (you can slice a sandwich with three parts (bread, ham, bread) with a straight planar cut s so that each slice is cut cut in two. Also we give an application to the ontinuum: the plane is different (not homeomorphic) 3 dimensional space. This is part of a beginner's course on Algebraic Topology, given by Assoc Prof NJ Wildberger of UNSW.
AlgTop2c: Homeomorphism and the group structure on a circle (cont.) This is the third video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic. Then we introduce the group structure on a circle, or in fact a general conic, in a novel way. This gives a gentle intro to the definition of a group. It also uses Pascal's theorem in an interesting way, so we give some background on projective geometry.
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-
AlgTop1d: One-dimensional objects (last) This is the fourth video of the first lecture of this beginner's course in Algebraic Topology. Here we begin to introduce basic one dimensional objects, namely the line and the circle. However each can appear in rather a remarkable variety of different ways.
AlgTop2e: Homeomorphism and the group structure on a circle (cont.) This is the fifth video of the second lecture in this beginner's course on Algebraic Topology. We give the basic definition of homeomorphism between two topological spaces, and explain why the line and circle are not homeomorphic. Then we introduce the group structure on a circle, or in fact a general conic, in a novel way. This gives a gentle intro to the definition of a group. It also uses Pascal's theorem in an interesting way, so we give some background on projective geometry.
AlgTop1: One-dimensional objects This is the first lecture of this beginner's course in Algebraic Topology (after the Introduction). In it we introduce the two basic one-dimensional objects: the line and circle. The latter has quite a few different manifestations: as a usual Euclidean circle, as the projective line of one-dimensional subspaces of a two-dimensional space, as a polygon, or as a space of orbits of a translation group on the line. This course is given by Assoc Prof NJ WIldberger of the School of Mathematics and Statistics at UNSW. See also his series on Rational Trigonometry (WildTrig) and Foundations of Mathematics (MathFoundations) as well as Linear Algebra (WildLinAlg) at YouTube user: njwildberger.
homeomorphism: [2011-05-23 13:24:18] Dark Energy Confirmed By Australian WiggleZ Sky Scan http://bit.ly/jfUrtm