Properties of topological spaces | Algebraic topology

Simply connected at infinity

In topology, a branch of mathematics, a topological space X is said to be simply connected at infinity if for any compact subset C of X, there is a compact set D in X containing C so that the induced map is the zero map. Intuitively, this is the property that loops far away from a small subspace of X can be collapsed, no matter how bad the small subspace is. The Whitehead manifold is an example of a 3-manifold that is contractible but not simply connected at infinity. Since this property is invariant under homeomorphism, this proves that the Whitehead manifold is not homeomorphic to R3. However, it is a theorem of John R. Stallings that for , a contractible n-manifold is homeomorphic to Rn precisely when it is simply connected at infinity. (Wikipedia).

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Infinity

This video provides a description of infinity with several examples. http://mathispower4u.com

From playlist Linear Inequalities in One Variable Solving Linear Inequalities

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Touching Infinity: It's Not Out of Reach

The conventional way to represent the Real Number system is to think of the numbers as corresponding to points along an infinite straight line. The problem is that in this representation there is no place for "infinity". Infinity is not a real number. This video shows an alternate visua

From playlist Lessons of Interest on Assorted Topics

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What is infinity ?

Definition of infinity In this video, I define the concept of infinity (as used in analysis), and explain what it means for sup(S) to be infinity. In particular, the least upper bound property becomes very elegant to write down. Check out my real numbers playlist: https://www.youtube.co

From playlist Real Numbers

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What is infinity?

What’s the biggest number you can think of? Well, what about one more than that number? We can’t really comprehend the idea of infinity, but it’s still a useful concept in science. Brian Greene explains more. Subscribe to our YouTube Channel for all the latest from World Science U. Visit

From playlist Science Unplugged: Physics

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A lot. List with links: http://vihart.com/how-many-kinds-of-infinity-are-there/

From playlist Doodling in Math and more | Math for fun and glory | Khan Academy

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Touching Infinity

How to visualize infinity in concrete terms.

From playlist Summer of Math Exposition 2 videos

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Can You Define the Immeasurable?

What is infinity? Can you define something that, by definition, has no boundaries? A subject extensively studied by philosophers, mathematicians, and more recently, physicists and cosmologists, infinity still stands as an enigma of the intellectual world. We asked people from all walks of

From playlist Mathematics

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Infinity - Sixty Symbols

It's a concept which intrigues mathematicians, but scientists aren't so keen on it. More at http://www.sixtysymbols.com/

From playlist From Sixty Symbols

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How to Compare Infinities

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From playlist Infinity, and Beyond!

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Higher Algebra 8: Spectra

In this video, we introduce and discuss spectra (in the sense of homotopy theory). We explain how they generalise abelian groups. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further informa

From playlist Higher Algebra

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Anna Miriam Benini: Polynomial versus transcendental dynamics

HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 24, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM

From playlist Dynamical Systems and Ordinary Differential Equations

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Lecture 8: Bökstedt Periodicity

In this video, we give a proof of Bökstedts fundamental result showing that THH of F_p is polynomial in a degree 2 class. This will rely on unlocking its relation to the dual Steenrod algebra and the fundamental fact, that the latter is free as an E_2-Algebra. Feel free to post comments a

From playlist Topological Cyclic Homology

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Cherkis 2021 04 05Yang-Mills Instantons, Quivers and Bows - Sergey Cherkis

Analysis Seminar Topic: Yang-Mills Instantons, Quivers and Bows Speaker: Sergey Cherkis Affiliation: University of Arizona; Member, School of Mathematics Date: April 05, 2021 For more video please visit http://video.ias.edu

From playlist Mathematics

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J. Wang - Topological rigidity and positive scalar curvature

In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with positive scalar curvature is homeomorphic to the Euclidean 3-space. We will furthermore explain the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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Developments in 4-manifold topology arising from a theorem of Donaldson's - John Morgan [2017]

slides for this talk: https://drive.google.com/file/d/1_wHviPab9klzwE4UkCOvVecyopxDsZA3/view?usp=sharing Name: John Morgan Event: Workshop: Geometry of Manifolds Event URL: view webpage Title: Developments in 4-manifold topology arising from a theorem of Donaldson's Date: 2017-10-23 @9:3

From playlist Mathematics

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Lecture 17: Frobenius lifts and group rings

In this video, we "compute" TC of spherical group rings and more generally cyclotomic spectra with Frobenius lifts. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://

From playlist Topological Cyclic Homology

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Lecture 11: Negative Topological cyclic homology

Correction: In the definition of stable ∞-categories at the very beginning, we forgot the condition that C has a zero object, i.e. the initial and terminal objects agree via the canonical morphism between them. Sorry for the confusion! In this video we define negative topological cyclic h

From playlist Topological Cyclic Homology

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J. Wang - Topological rigidity and positive scalar curvature (version temporaire)

In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with positive scalar curvature is homeomorphic to the Euclidean 3-space. We will furthermore explain the

From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics

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Introduction to Limits at Infinity (Part 1)

This video introduces limits at infinity. https://mathispower4u.com

From playlist Limits at Infinity and Special Limits

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Lecture 10: The circle action on THH

In this video we construct an action of the circle group S^1 = U(1) on the spectrum THH(R). We will see how this is the homotopical generalisation of the Connes operator. The key tool will be Connes' cyclic category. The speaker is of course Achim Krause and not Thomas Nikolaus as falsely

From playlist Topological Cyclic Homology

Related pages

Compact space | Topological space | Manifold | Homeomorphism | Topology | Whitehead manifold