Disjoint union (topology)

Topology: Connectedness

This video is about connectedness and some of its basic properties.

From playlist Basics: Topology

MAST30026 Lecture 7: Constructing topological spaces (Part 2)

I defined the disjoint union of topological spaces, quotient spaces and the pushout. Lecture notes: http://therisingsea.org/notes/mast30026/lecture7.pdf The class webpage: http://therisingsea.org/post/mast30026/ Have questions? I hold free public online office hours for this class, every

From playlist MAST30026 Metric and Hilbert spaces

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 are Disjoint Sets? | Set Theory

What are disjoint sets? That is the topic of discussion in today's lesson! Two sets, A and B, are disjoint if and only if A intersect B is equal to the empty set. This means that two sets are disjoint if and only if they have no elements in common. This is the same as the two sets being "m

From playlist Set Theory

Dihedral Group (Abstract Algebra)

The Dihedral Group is a classic finite group from abstract algebra. It is a non abelian groups (non commutative), and it is the group of symmetries of a regular polygon. This group is easy to work with computationally, and provides a great example of one connection between groups and geo

From playlist Abstract Algebra

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

Abstract Algebra | The dihedral group

We present the group of symmetries of a regular n-gon, that is the dihedral group D_n. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Abstract Algebra

22 Combinations of binary operations

The left- and right distributive properties of the combination of binary operations.

From playlist Abstract algebra

MAST30026 Lecture 7: Constructing topological spaces (Part 3)

Today's lecture was all about examples, constructed using the disjoint union, quotient and pushouts from last lecture. These examples includes the torus, Mobius band, and finally arbitrary CW complexes. Lecture notes: http://therisingsea.org/notes/mast30026/lecture7.pdf The class webpage:

From playlist MAST30026 Metric and Hilbert spaces

MAST30026 Lecture 11: Hausdorff spaces (Part 1)

I introduced the Hausdorff condition, proved some basic properties, discussed the "real line with a double point" as an example of a non-Hausdorff space, proved that a compact subspace of a Hausdorff space is closed, and that continuous bijections from compact to Hausdorff spaces are homeo

From playlist MAST30026 Metric and Hilbert spaces

Commutative algebra 13 (Topology of Spec R)

This lecture is part of an online course on commutative algebra, following the book "Commutative algebra with a view toward algebraic geometry" by David Eisenbud. In this lecture we discuss the topology of the spectrum Spec R of a ring, showing that it is compact, sometimes connected, an

From playlist Commutative algebra

Higher Algebra 10: E_n-Algebras

In this video we introduce E_n-Algebras in arbitrary symmetric monoidal infinity-categories. These interpolate between associated algebras (= E_1) and commutative algebras (= E_infinity). We also establish some categorical properties and investigate the case of the symmetric monoidal infin

From playlist Higher Algebra

Dustin Clausen - Toposes generated by compact projectives, and the example of condensed sets

Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ The simplest kind of Grothendieck topology is the one with only trivial covering sieves, where the associated topos is equal to the presheaf topos. The next simplest topology ha

From playlist Toposes online

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

Benson Farb, Part 3: Reconstruction problems in geometry and topology

29th Workshop in Geometric Topology, Oregon State University, June 30, 2012

From playlist Benson Farb: 29th Workshop in Geometric Topology

What is a Manifold? Lesson 1: Point Set Topology and Topological Spaces

This will begin a short diversion into the subject of manifolds. I will review some point set topology and then discuss topological manifolds. Then I will return to the "What is a Tensor" series. It has been well over a year since we began this project. We now have a Patreon Page: https

From playlist What is a Manifold?

Danny Calegari: Big Mapping Class Groups - lecture 2

Part I - Theory : In the "theory" part of this mini-course, we will present recent objects and phenomena related to the study of big mapping class groups. In particular, we will define two faithful actions of some big mapping class groups. The first is an action by isometries on a Gromov-h

From playlist Topology

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?

Continuity in Topology

In this video, I cover the notion of continuity, as used in topology. The beautiful thing is that this doesn't use epsilon-delta at all, and instead just something purely geometric. Enjoy this topology-adventure! Topology Playlist: https://youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGG

From playlist Topology