I define closed sets, an important notion in topology and analysis. It is defined in terms of limit points, and has a priori nothing to do with open sets. Yet I show the important result that a set is closed if and only if its complement is open. More topology videos can be found on my pla
From playlist Topology
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
Nested Interval Property and Proof | Real Analysis
We introduce and prove the nested interval property, or nested interval theorem, or NIP, whatever you like to call it. This theorem says that, given a sequence of nested and closed intervals, that is, closed intervals J1, J2, J3, and so on such that each Jn contains Jn+1, this infinite seq
From playlist Real Analysis
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
Topology 1.3 : Basis for a Topology
In this video, I define what a basis for a topology is. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
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
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?
Topology: Interior, Exterior and Boundary
This video is about the interior, exterior, and boundary of sets.
From playlist Basics: Topology
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?
In this video, I introduce the order topology and prove that it is Hausdorff. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology
Real Analysis Ep 13: Open sets
Episode 13 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about open sets of real numbers. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://fac
From playlist Math 3371 (Real analysis) Fall 2020
Robin Deeley: The K-theory of the stable algebra and stable Ruelle algebra of a Wieler solenoid
Talk by Robin Deeley in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on May 13, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Ashani Dasgupta: Local Connectedness of Boundaries for Relatively Hyperbolic Groups
Ashani Dasgupta, University of Wisconsin-Milwaukee Title: Local Connectedness of Boundaries for Relatively Hyperbolic Groups Let $(\Gamma,\mathbb{P})$ be a relatively hyperbolic group pair that is relatively one ended. Then the Bowditch boundary of $(\Gamma,\mathbb{P})$ is locally connect
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Justin Curry (6/2/20): Counting embedded spheres with the same persistence
Title: Counting embedded spheres with the same persistence Abstract: In this talk I extend earlier collaborative work with Catanzaro, Fasy, Lazovskis, Malen, Reiss, Wang and Zabka (https://arxiv.org/abs/1909.10623) on inverse problems in Topological Data Analysis. In this new work with my
From playlist SIAM Topological Image Analysis 2020
Gregory Henselman-Petrusek (9/28/22): Saecular persistence
Homology with field coefficients has become a mainstay of modern TDA, thanks in part to structure theorems which decompose the corresponding persistence modules. This naturally begs the question -- what of integer coefficients? Or homotopy? We introduce saecular persistence, a categoric
From playlist AATRN 2022
Algebraic and topological models for DNA recombination - Nataša Jonoska
Workshop on Topology: Identifying Order in Complex Systems Algebraic and topological models for DNA recombination Nataša Jonoska University of South Florida Date: November 6, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Math 101 Fall 2017 102517 Monotonic Sequences; Bolzano Weierstrass Theorem
Brief comments about monotonic sequences. Monotonic Sequence Theorem. Unbounded monotonic sequences converges to infinity. Bolzano-Weierstrass theorem: topological definitions (neighborhood, punctured neighborhood); accumulation point; examples. Statement and proof of Bolzano-Weierstra
From playlist Course 6: Introduction to Analysis (Fall 2017)
This video defines set-builder notation and compares it to interval expressed graphically, using interval notation, and using inequalities. Site: http://mathispower4u.com
From playlist Using Interval Notation
Manfred Madritsch: Normal and Non-Normal Numbers
CIRM HYBRID EVENT Recorded during the meeting " Diophantine Problems, Determinism and Randomness" the February 04, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathem
From playlist Probability and Statistics
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