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
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
Geometry: Introduction to the Polygon (quadrilateral, pentagon, hexagon and more)
Learn the definition of polygon - a very important shape in geometry. When a polygon has a small number of sides, there is a word you use instead of "polygon". We teach you the names of polygons with 3 to 10 sides. To learn more Geometry, you can watch our playlist from the beginning:
From playlist Euclidean Geometry
Topology 1.6 : Metric Topology
In this video, I introduce the metric topology, and introduce how the topologies it generates align with the standard topologies on Euclidean space. Email : fematikaqna@gmail.com Subreddit : https://www.reddit.com/r/fematika Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric
From playlist Topology
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
Algebraic Topology - 5.1 - Mappings Spaces and the Compact Open Topology
We define the compact open topology on mapping spaces.
From playlist Algebraic Topology
Topological Spaces: The Subspace Topology
Today, we discuss the subspace topology, which is a useful tool to construct new topologies.
From playlist Topology & Manifolds
What is a Manifold? Lesson 4: Countability and Continuity
In this lesson we review the idea of first and second countability. Also, we study the topological definition of a continuous function and then define a homeomorphism.
From playlist What is a Manifold?
Today, we begin the manifolds series by introducing the idea of a topological manifold, a special type of topological space which is locally homeomorphic to Euclidean space.
From playlist Manifolds
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?
Johnathan Bush (11/5/21): Maps of Čech and Vietoris–Rips complexes into euclidean spaces
We say a continuous injective map from a topological space to k-dimensional euclidean space is simplex-preserving if the image of each set of at most k+1 distinct points is affinely independent. We will describe how simplex-preserving maps can be useful in the study of Čech and Vietoris–Ri
From playlist Vietoris-Rips Seminar
What is a Manifold? Lesson 3: Separation
He we present some alternative topologies of a line interval and then discuss the notion of separability. Note the error at 4:05. Sorry! If you are viewing this on a mobile device, my annotations are not visible. This is due to a quirck of YouTube.
From playlist What is a Manifold?
Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri (L1) by Sunil Mukhi
Seminar Lecture Series - Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri Speaker: Sunil Mukhi (IISER Pune) Date : Mon, 20 March 2023 to Fri, 21 April 2023 Venue: Online (Zoom & Youtube) ICTS is pleased to announce special lecture series by Prof. Sunil Mukh
From playlist Lecture Series- Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri -2023
Jürgen Jost (5/13/22): Geometry and Topology of Data
We link the basic concept of topological data analysis, intersection patterns of distance balls, with geometric concepts. The key notion is hyperconvexity, and we also explore some variants. Hyperconvexity in turn leads us to a new concept of generalized curvature for metric spaces. Curvat
From playlist Bridging Applied and Quantitative Topology 2022
Manifolds - Part 9 - Locally Euclidean Spaces
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics Or via Patreon: https://www.patreon.com/bsom Or via other methods: https://thebrightsideofmathematics.
From playlist Manifolds
Manifolds - Part 9 - Locally Euclidean Spaces [dark version]
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Or via Ko-fi: https://ko-fi.com/thebrightsideofmathematics Or via Patreon: https://www.patreon.com/bsom Or via other methods: https://thebrightsideofmathematics.
From playlist Manifolds [dark version]
Jürgen Jost (8/29/21): Geometry and Topology of Data
Data sets are often equipped with distances between data points, and thereby constitute a discrete metric space. We develop general notions of curvature that capture local and global properties of such spaces and relate them to topological concepts such as hyperconvexity. This also leads t
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
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