Path (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

Connectedness

In this video, I define connectedness, which is a very important concept in topology and math in general. Essentially, it means that your space only consists of one piece, whereas disconnected spaces have two or more pieces. I also define the related notion of path-connectedness. Topology

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

What is a Path? | Graph Theory

What is a path in the context of graph theory? We go over that in today's math lesson! We have discussed walks, trails, and even circuits, now it is about time we get to paths! Recall that a walk is a sequence of vertices in a graph, such that consecutive vertices are adjacent. A path is t

From playlist Graph Theory

Section 4b: Graph Connectivity

From playlist Graph Theory

What is a Path Graph? | Graph Theory

What is a path graph? We have previously discussed paths as being ways of moving through graphs without repeating vertices or edges, but today we can also talk about paths as being graphs themselves, and that is the topic of today's math lesson! A path graph is a graph whose vertices can

From playlist Graph Theory

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

Longest Simple Path - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Find the Shortest Path - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Lie Groups and Lie Algebras: Lesson 34 -Introduction to Homotopy

Lie Groups and Lie Algebras: Introduction to Homotopy In order to proceed with Gilmore's study of Lie groups and Lie algebras we now need a concept from algebraic topology. That concept is the notion of homotopy and the Fundamental Group of a topological space. In this lecture we provide

From playlist Lie Groups and Lie Algebras

What is a Manifold? Lesson 5: Compactness, Connectedness, and Topological Properties

The last lesson covering the topological prep-work required before we begin the discussion of manifolds. Topics covered: compactness, connectedness, and the relationship between homeomorphisms and topological properties.

From playlist What is a Manifold?

Lie Groups and Lie Algebras: Lesson 37 - The Fundamental Groups of SU(2) and SO(3)

Lie Groups and Lie Algebras: Lesson 37 - Homotopy Groups of SU(2) and SO(3) In this lesson we discover the Fundamental Group of SU(2) and S0(3) and learn the critical fact that they are not the same. That is, the Fundamental Group associated with the topological space SU(2) is simply conn

From playlist Lie Groups and Lie Algebras

Clark Barwick - 2/3 Exodromy for ℓ-adic Sheaves

In joint work with Saul Glasman and Peter Haine, we proved that the derived ∞-category of constructible ℓ-adic sheaves ’is’ the ∞-category of continuous functors from an explicitly defined 1-category to the ∞-category of perfect complexes over ℚℓ. In this series of talks, I want to offer s

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the concept of a Universal Covering Group

Lie Groups and Lie Algebras: Lesson 38 - Preparation for the Universal Covering Group concept In this lesson we examine another amazing connection between the algebraic properties of the Lie groups with topological properties. We will lay the foundation to understand how discrete invaria

From playlist Lie Groups and Lie Algebras

What is a Manifold? Lesson 18: Homotopy

What is a Manifold? Lesson 18: Introduction to Homotopy

From playlist What is a Manifold?

José Manuel García-Calcines (6/24/21): Topological complexity using arbitrary covers

Title: Topological complexity using arbitrary covers

From playlist Topological Complexity Seminar

Emilie Purvine (5/2/21): Homology of Graphs and Hypergraphs

Graphs and hypergraphs are typically studied from a combinatorial perspective. A graph being a collection of vertices and pairwise relationships (edges) among the vertices, and a hypergraph capturing multi-way or groupwise relationships (hyperedges) among the vertices. But both of these ob

From playlist TDA: Tutte Institute & Western University - 2021

Algebraic topology: Introduction

This lecture is part of an online course on algebraic topology. This is an introductory lecture, where we give a quick overview of some of the invariants of algebraic topology (homotopy groups, homology groups, K theory, and cobordism). The book "algebraic topology" by Allen Hatcher men

From playlist Algebraic topology

Jezus Gonzalez (6/25/17) Bedlewo: Topological complexity and the motion planning problem in robotics

Early this century Michael Farber introduced the concept of Topological Complexity (TC), a model to study the continuity instabilities in the motion planning problem in robotics. Farber’s model has captured much attention since then due to the rich algebraic topology properties encoded by

From playlist Applied Topology in Będlewo 2017

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