Final 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

What is a closed set ?

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 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

Topology 1.4 : Product Topology Introduction

In this video, I define the product topology, and introduce the general cartesian product. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet

From playlist Topology

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 1.5 : Order Topology

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

Topology: Interior, Exterior and Boundary

This video is about the interior, exterior, and boundary of sets.

From playlist Basics: Topology

What Is Network Topology? | Types of Network Topology | BUS, RING, STAR, TREE, MESH | Simplilearn

In this video on Network Topology, we will understand What is Network topology, the role of using topology while designing a network, Different types of Topologies in a Network. Network topology provides us with a way to configure the most optimum network design according to our requiremen

From playlist Cyber Security Playlist [2023 Updated]🔥

Bárbara M. Gutiérrez (7/22/21): Effectual topological complexity

In this talk we will introduce the concept of Effectual Topological Complexity, which is a new version of the Topological Complexity (TC) for G-Spaces. We will state some of its main properties, for instance, we will explain the relation between this notion with the standard version of TC

From playlist Topological Complexity Seminar

What is a Manifold? Lesson 14: Quotient Spaces

I AM GOING TO REDO THIS VIDEO. I have made some annotations here and annotations are not visible on mobile devices. STAY TUNED. This is a long lesson about an important topological concept: quotient spaces.

From playlist What is a Manifold?

Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS

The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t

From playlist Introduction to Homotopy Theory

Hengrui Luo (4/22/20): Lower dimensional topological information: Theory and applications

Title: Lower dimensional topological information: Theory and applications Abstract: Topological data analysis (TDA) allows us to explore the topological features of a dataset. Among topological features, lower dimensional ones are of growing interest in mathematics and statistics due to t

From playlist AATRN 2020

Lecture 7: Sheaves of sets (Part 2)

The most important examples of topoi are categories of sheaves of sets on a small category. Patrick Eilliott introduced this class of examples over two talks, of which is the second. In this talk he defines Grothendieck topologies and the category of sheaves on a site, and develops the exa

From playlist Topos theory seminar

Geometric Representation of Structured Extensions in Ergodic Theory - Henrik Kreidler

Special Year Research Seminar Topic: Geometric Representation of Structured Extensions in Ergodic Theory Speaker: Henrik Kreidler Affiliation: Bergische Universität Wuppertal Date: March 14, 2023 The Mackey-Zimmer representation theorem is a key structural result from ergodic theory: Eve

From playlist Mathematics

Morgan Rogers - Toposes of Topological Monoid Actions

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RogersSlidesToposesOnline.pdf We explain the properties of the familiar properties of continuous actions of groups o

From playlist Toposes online

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

Emergent topology in quenched quantum systems by Amit Dutta

DATES Monday 20 Jun, 2016 - Wednesday 29 Jun, 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore APPLY Understanding strongly interacting quantum many body systems is one of the major frontiers in present day physics. Condensed matter physics provides a wide panoply of systems where strong

From playlist School on Current Frontiers in Condensed Matter Research

Definition of a Topological Space

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space

From playlist Topology

Enrique Macias-Virgo (5/27/21): Homotopic distance and Generalized motion planning

Lusternik-Schnirelmann category and topological complexity are particular cases of a more general notion, that we call homotopic distance between two maps. As a consequence, several properties of those invariants can be proved in a unified way and new results arise. For instance, we prove

From playlist Topological Complexity Seminar