General topology | Properties of topological spaces
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space is a connected set if it is a connected space when viewed as a subspace of . Some related but stronger conditions are , simply connected, and -connected. Another related notion is locally connected, which neither implies nor follows from connectedness. (Wikipedia).
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From playlist Science Unplugged: Special Relativity
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
In this video, I define connectedness, which is a very important concept in topology and math in general. Essentially, it means that your space only consists of one piece, whereas disconnected spaces have two or more pieces. I also define the related notion of path-connectedness. Topology
From playlist Topology
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
This video is about connectedness and some of its basic properties.
From playlist Basics: Topology
If the universe is spatially infinite, what can we say about reality...
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From playlist Science Unplugged: Cosmology
What is a Manifold? Lesson 5: Compactness, Connectedness, and Topological Properties
The last lesson covering the topological prep-work required before we begin the discussion of manifolds. Topics covered: compactness, connectedness, and the relationship between homeomorphisms and topological properties.
From playlist What is a Manifold?
Is there any place in the Universe where there's truly nothing? Consider the gaps between stars and galaxies? Or the gaps between atoms? What are the properties of nothing?
From playlist Guide to Space
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From playlist Science Unplugged: Parallel Universes
Higher solutions of Hitchin’s selfduality equations and real sections by Sebastian Heller
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From playlist Analytic and Algebraic Geometry-2018
Moduli space of regular singular parabolic connections and isomonodromic deformation by M.Inaba
Program :Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
Metric Spaces - Lectures 15 & 16: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 8th of 11 videos. The course is about the notion of distance. You ma
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Conformal Limits of Parabolic Higgs Bundles by Richard Wentworth
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From playlist Vortex Moduli - 2023
Metric Spaces - Lectures 17 & 18: Oxford Mathematics 2nd Year Student Lecture
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From playlist Oxford Mathematics Student Lectures - Metric Spaces
What is General Relativity? Lesson 9: Parallelism and the Covariant Derivative
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From playlist What is General Relativity?
Lie Groups and Lie Algebras: Lesson 38 - Preparation for the concept of a Universal Covering Group
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From playlist Lie Groups and Lie Algebras
Sergio Zamora (1/20/23): The lower semi-continuity of \pi_1 and nilpotent structures in persistence
When a sequence of compact geodesic spaces X_i converges to a compact geodesic space X, under minimal assumptions there are surjective morphisms $\pi_1(X_i) \to \pi_1(X)$ for i large enough. In particular, a limit of simply connected spaces is simply connected. This is clearly not true for
From playlist Vietoris-Rips Seminar
Moduli spaces of parabolic connections and parabolic bundles and Geometric Langlands by M-H Saito
Program: Quantum Fields, Geometry and Representation Theory ORGANIZERS : Aswin Balasubramanian, Saurav Bhaumik, Indranil Biswas, Abhijit Gadde, Rajesh Gopakumar and Mahan Mj DATE & TIME : 16 July 2018 to 27 July 2018 VENUE : Madhava Lecture Hall, ICTS, Bangalore The power of symmetries
From playlist Quantum Fields, Geometry and Representation Theory
PowerShell+ 2019 - PowerShell Remoting Internals by Paul Higinbotham
PowerShell remoting is essential for automation. It began as a way to fan out scripts to multiple target machines over WinRM. But there is now PowerShell Direct for WinRM-less connections between host and guest VMs, and you can make remote IPC connections to any local process hosting Power
From playlist PowerShell + DevOps Global Summit 2019