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: Interior, Exterior and Boundary
This video is about the interior, exterior, and boundary of sets.
From playlist Basics: 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
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
Finding Closed Sets, the Closure of a Set, and Dense Subsets Topology
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding Closed Sets, the Closure of a Set, and Dense Subsets Topology
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
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
The Homework Problem That Started as a Phd Thesis: 14 set theorem
In a handful of introductory topology textbooks, Kuratowski's 14 set theorem is given as an exercise despite it being one of the results proven as a part of his phd thesis in 1922. This homework problem that started out as a phd thesis is not an easy exercise if you don't know how to think
From playlist The New CHALKboard
What is a Manifold? Lesson 2: Elementary Definitions
This lesson covers the basic definitions used in topology to describe subsets of topological spaces.
From playlist What is a Manifold?
Antonio Rieser (03/29/23) Algebraic Topology for Graphs & Mesoscopic Spaces: Homotopy & Sheaf Theory
Title: Algebraic Topology for Graphs and Mesoscopic Spaces: Homotopy and Sheaf Theory Abstract: In this talk, we introduce the notion of a mesoscopic space: a metric space decorated with a privileged scale, and we survey recent developments in the algebraic topology of such spaces. Our ap
From playlist AATRN 2023
Infinite Intersection of Open Sets that is Closed Proof
Infinite Intersection of Open Sets that is Closed Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Topology
What is the Mordell-Lang problem?
It is my intention to eventually explain some things about the Mordell-Lang problem and the higher dimensional versions of these. The presentation in this video is due to Mazur and can be found in an MSRI article he wrote that introduces these things.
From playlist Mordell-Lang
MAST30026 Lecture 13: Metrics on function spaces (Part 1)
I defined the sup metric on the function space Cts(X,Y) where X is compact and Y is a metric space, and proved that the associated metric topology agrees with the compact-open topology. Lecture notes: http://therisingsea.org/notes/mast30026/lecture13.pdf The class webpage: http://therisi
From playlist MAST30026 Metric and Hilbert spaces
Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri (L3) 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
Galois theory: Algebraic closure
This lecture is part of an online graduate course on Galois theory. We define the algebraic closure of a field as a sort of splitting field of all polynomials, and check that it is algebraically closed. We hen give a topological proof that the field C of complex numbers is algebraically
From playlist Galois theory
Markus Haase : Operators in ergodic theory - Lecture 3 : Compact semigroups and splitting theorems
Abstract : The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems Recording during the thematic meeting : "Probabilistic Aspects of Multiple Ergodic Averages " the December 8
From playlist Dynamical Systems and Ordinary Differential Equations
Abstraction - Seminar 2 - Resolution I, blowing up
This seminar series is on the relations among Natural Abstraction, Renormalisation and Resolution. This week Daniel Murfet gives an introduction to blowing up an affine algebraic variety at a point. The webpage for this seminar is https://metauni.org/abstraction/ You can join this semina
From playlist Abstraction
BAG1.1. Toric Varieties 1 - Affine Varieties over C
Edit: Not quite a typo at 4:45: for the V function, we have V(I n J)=V(I) u V(J). The vanishing points are unchanged if we replace V(I n J) with V(IJ), but if you get into the scheme game, there's a difference. See links in the comments. Basic Algebraic Geometry: We define affine variet
From playlist Basic Algebraic Geometry
Closed Intervals, Open Intervals, Half Open, Half Closed
00:00 Intro to intervals 00:09 What is a closed interval? 02:03 What is an open interval? 02:49 Half closed / Half open interval 05:58 Writing in interval notation
From playlist Calculus