What are Overlapping Sets? | Set Theory
What are overlapping sets? This is a relation between sets that I have not seen any YouTube videos on, so I figured I'd add this video explaining the term to the massive YouTube catalogue! In this video we define overlapping sets and give some examples. Two sets, A and B, are overlapping
From playlist Set Theory
My submission for the Summer of Math Exposition competition: https://www.youtube.com/watch?v=ojjzXyQCzso An introduction to the idea behind the mathematical definition of continuity. If you are familiar with the epsilon-delta definition of continuity, you may recognise it here, where I
From playlist Summer of Math Exposition Youtube Videos
Topology (What is a Topology?)
What is a Topology? Here is an introduction to one of the main areas in mathematics - Topology. #topology Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, b
From playlist Topology
In this video, I cover the notion of continuity, as used in topology. The beautiful thing is that this doesn't use epsilon-delta at all, and instead just something purely geometric. Enjoy this topology-adventure! Topology Playlist: https://youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGG
From playlist Topology
Topology 1.1 : Open Sets of Reals
In this video, I give a definition of the open sets on the real numbers. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Algebraic Topology - 5.3 - Mapping Spaces and the Compact Open Topology
Description of the adjunction (X \times -, Top(X,-))
From playlist Algebraic Topology
Bala Krishnamoorthy (2/11/2020): An Introduction to Mapper
Title: An Introduction to Mapper Abstract: The Mapper construction has recently become one of the main faces of topological data analysis (TDA), especially from the point of view of diverse applications. It is a data visualization technique that is rather straightforward to describe and i
From playlist Tutorials
The mapper algorithm and Reeb graphs
Title: The mapper algorithm and Reeb graphs Abstract: This tutorial gives an introduction to the mapper algorithm in applied topology. The mapper algorithm can be thought of as an approximation of a Reeb graph of a space, when given only a finite data set sampled from that space. Please s
From playlist Tutorials
Topology 1.7 : More Examples of Topologies
In this video, I introduce important examples of topologies I didn't get the chance to get to. This includes The discrete and trivial topologies, subspace topology, the lower-bound and K topologies on the reals, the dictionary order, and the line with two origins. I also introduce (again)
From playlist Topology
Topology: Interior, Exterior and Boundary
This video is about the interior, exterior, and boundary of sets.
From playlist Basics: Topology
Manifolds - Part 2 - Interior, Exterior, Boundary, Closure
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From playlist Manifolds
Manifolds - Part 2 - Interior, Exterior, Boundary, Closure [dark version]
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From playlist Manifolds [dark version]
In this video, I discuss the notion of sequential compactness, which is an important concept used in topology and analogy. I also explain the similarities and differences between sequential compactness and covering compactness. Compactness: https://youtu.be/xiWizwjpt8o Bolzano-Weierstrass
From playlist Topology
What is a Manifold? Lesson 6: Topological Manifolds
Topological manifolds! Finally! I had two false starts with this lesson, but now it is fine, I think.
From playlist What is a Manifold?
What_is_a_Manifold_Lesson_16: The Mobius strip
What is a Manifold? Lesson 16: The Mobius strip The Mobius strip is a quotient space, a manifold, and a fiber bundle. In this lecture we define the Mobius strip as a quotient space and prove that it is a manifold.
From playlist What is a Manifold?
What is a Manifold? Lesson 13: The tangent bundle - an illustration.
What is a Manifold? Lesson 13: The tangent bundle - an illustration. Here we have a close look at a complete example using the tangent bundle of the manifold S_1. Next lesson we look at the Mobius strip as a fiber bundle.
From playlist What is a Manifold?
Introduction to Homotopy Theory- PART 2: (TOPOLOGICAL) HOMOTOPY
We move on to the second section of nLab's introduction to homotopy theory, homotopy. Topics covered include left/right homotopy, topolocial path/cylinder objects, homotopy groups, and weak/standard homotopy equivalences. PLEASE leave any misconceptions I had or inaccuracies in my video i
From playlist Introduction to Homotopy Theory
Professor Gunnar Carlsson , Stanford University, USA
From playlist Public Lectures
This video is about continuity and some of its basic properties.
From playlist Basics: Topology
Who Gives a Sheaf? Part 2: A non-example
In this video we compare two pre-sheaves, one which is a sheaf, and one which is not.
From playlist Who Gives a Sheaf?