Topological spaces

Excluded point topology

In mathematics, the excluded point topology is a topology where exclusion of a particular point defines openness. Formally, let X be any non-empty set and p ∈ X. The collection of subsets of X is then the excluded point topology on X. There are a variety of cases which are individually named: * If X has two points, it is called the Sierpiński space. This case is somewhat special and is handled separately. * If X is finite (with at least 3 points), the topology on X is called the finite excluded point topology * If X is countably infinite, the topology on X is called the countable excluded point topology * If X is uncountable, the topology on X is called the uncountable excluded point topology A generalization is the open extension topology; if has the discrete topology, then the open extension topology on is the excluded point topology. This topology is used to provide interesting examples and counterexamples. (Wikipedia).

Video thumbnail

Every Subset of the Discrete Topology has No Limit Points Proof

Every Subset of the Discrete Topology has No Limit Points 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

Video thumbnail

Finding Limit Points and the Derived Set in a Topological Space

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding Limit Points and the Derived Set in a Topological Space

From playlist Topology

Video thumbnail

How to Find the Limit Points and Derived Set of a Subset in a Topology

How to Find the Limit Points and Derived Set of a Subset in a Topology 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

Video thumbnail

Hausdorff Example 1: Cofinite Topology

Point Set Topology: We recall the notion of a Hausdorff space and consider the cofinite topology as a source of non-Hausdorff examples. We also note that this topology is always compact.

From playlist Point Set Topology

Video thumbnail

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

Video thumbnail

Topology: Interior, Exterior and Boundary

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

From playlist Basics: Topology

Video thumbnail

Definition of a Topological Space

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

From playlist Topology

Video thumbnail

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

Video thumbnail

Five Stages of Accepting Constructive Mathematics - Andrej Bauer

Andrej Bauer University of Ljubljana, Slovenia; Member, School of Mathematics March 18, 2013 Discussions about constructive mathematics are usually derailed by philosophical opinions and meta-mathematics. But how does it actually feel to do constructive mathematics? A famous mathematician

From playlist Mathematics

Video thumbnail

Limit Points

Limit Points In this video, I define the notion of a limit point (also known as a subsequential limit) and give some examples of limit points. Limit points are closed: https://youtu.be/b1jYloJXDYY Check out my Sequences Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCuFxFs

From playlist Sequences

Video thumbnail

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

Video thumbnail

Geometry of Surfaces - Topological Surfaces Lecture 1 : Oxford Mathematics 3rd Year Student Lecture

This is the first of four lectures from Dominic Joyce's 3rd Year Geometry of Surfaces course. The four lectures cover topological surfaces and conclude with a big result, namely the classification of surfaces. This lecture provides an introduction to the course and to topological surfaces.

From playlist Oxford Mathematics Student Lectures - Geometry of Surfaces

Video thumbnail

Real Lagrangian Tori in toric symplectic manifolds - Joé Brendel

IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Real Lagrangian Tori in toric symplectic manifolds Speaker:Joé Brendel Affiliation: University of Neuchâte Date: June 4, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Topology Without Tears - Video 4c - Writing Proofs in Mathematics

This is part (c) of the fourth video in a series of videos which supplement my online book "Topology Without Tears" which is available free of charge at www.topologywithouttears.net Video 4 focusses on the extremely important topic of writing proofs. This video is about Proof by Contradict

From playlist Topology Without Tears

Video thumbnail

Coarse dynamics and partially hyperbolic diffeomorphisms in 3-manifolds - Rafael Potrie

Members' Seminar Topic: Coarse dynamics and partially hyperbolic diffeomorphisms in 3-manifolds Speaker: Rafael Potrie Affiliation: Universidad de la República, Uruguay; von Neumann Fellow, School of Mathematics Date: February 03, 2020 For more video please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

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?

Video thumbnail

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

Video thumbnail

SHM - 16/01/15 - Constructivismes en mathématiques - Marie Françoise Roy

Marie-Françoise Roy (IRMAR, Université Rennes 1), « Méthodes constructives en algèbre abstraite : l'exemple de la dimension »

From playlist Les constructivismes mathématiques - Séminaire d'Histoire des Mathématiques

Video thumbnail

Chi-Keung Ng: Ortho-sets and Gelfand spectra

Talk by Chi-Keung Ng in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on June 9, 2021

From playlist Global Noncommutative Geometry Seminar (Europe)

Video thumbnail

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

Related pages

Subset | Sierpiński space | Topological space | Finite topological space | List of topologies | Particular point topology | Counterexamples in Topology | Mathematics | Finite set | Alexandrov topology | Fort space | Open set