Topological space

Topology: Topological Spaces

This video is about topological spaces and some of their basic properties.

From playlist Basics: Topology

Definition of a Topological Space

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

From playlist Topology

Introduction to Metric Spaces

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

Topology: Metric Spaces

This video is about metric spaces and some of their basic properties.

From playlist Basics: Topology

What is a metric space ?

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

Topological Spaces: Introduction & Axioms

The first video in a new series on topological spaces and manifolds.

From playlist Topology & Manifolds

Metric spaces -- Proofs

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

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?

Topological Spaces: The Subspace Topology

Today, we discuss the subspace topology, which is a useful tool to construct new topologies.

From playlist Topology & Manifolds

Sanjay Mishra: Preservation of Properties during Topological Equivalence of Function Space

Sanjay Mishra, Lovely Professional University Title: Preservation of Properties during Topological Equivalence of Function Space The study of convergence of sequence of functions is the most important and active area of research in theoretical mathematics that solve several problems of app

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

SEPARATION BUT MATHEMATICALLY: What Types of Mathematical Topologies are there? | Nathan Dalaklis

The title of this video is a bit convoluted. What do you mean by "Separation but Mathematically"? Well, in this video I'll be giving a (very diluted) answer to the question "What types of mathematical topologies are there?" by introducing the separation axioms in topology. The separation

From playlist The New CHALKboard

Manifolds #1: Introduction

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 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?

MAST30026 Lecture 6: Topological spaces

In this lecture I defined topological spaces and continuous maps, explained how any metric space gives rise to a topological space, and proved that epsilon-delta continuity for functions between metric spaces agrees with the new notion of continuity. Lecture notes: http://therisingsea.org

From playlist MAST30026 Metric and Hilbert spaces

An Introduction to Topological Spaces [Lori Ziegelmeier]

This tutorial provides an introduction to topological spaces, including a brief overview of some of the central mathematicians to define a topology. The primary focus is on the set of the real line with various notions of topologies defined on this set. This tutorial was contributed as pa

From playlist Tutorial-a-thon 2021 Spring

What is a Manifold? Lesson 15: The cylinder as a quotient space

What is a Manifold? Lesson 15: The cylinder as a quotient space This lesson covers several different ideas on the way to showing how the cylinder can be described as a quotient space. Lot's of ideas in this lecture! ... too many probably....

From playlist What is a Manifold?

MAST30026 Lecture 7: Constructing topological spaces (Part 1)

I introduced the notion of a basis for a topology, defined the product of topological spaces and proved the universal property of the product. Lecture notes: http://therisingsea.org/notes/mast30026/lecture7.pdf The class webpage: http://therisingsea.org/post/mast30026/ Have questions? I

From playlist MAST30026 Metric and Hilbert spaces

Topological spaces and manifolds | Differential Geometry 24 | NJ Wildberger

We introduce the notion of topological space in two slightly different forms. One is through the idea of a neighborhood system, while the other is through the idea of a collection of open sets. While this is all reasonably traditional stuff, regular viewers of this channel will not be surp

From playlist Differential Geometry

MAST30026 Lecture 12: Function spaces (Part 2)

The aim of this lecture was to motivate the definition of the compact-open topology on function spaces, via the adjunction property. I explained how any topology making the adjunction property true must include a certain class of open sets, which we will define next lecture to be a sub-bas

From playlist MAST30026 Metric and Hilbert spaces