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
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
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
Gluing is a good method to construct new topological spaces from known ones. Here a rectangles is glued along the edges to form a torus. Often the fundamental group of the glued object can be calculated from the pieces (here a rectangles) and the glue (here two intersecting circles). Th
From playlist Algebraic Topology
In this video, I discuss what it means for a function in Rn to be continuous, and more generally about continuity in metric spaces. Moreover, I show that a function is continuous if and only if each component is continuous. Enjoy the metric space extravaganza! Every function is continuous
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
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 1.6 : Metric Topology
In this video, I introduce the metric topology, and introduce how the topologies it generates align with the standard topologies on Euclidean space. Email : fematikaqna@gmail.com Subreddit : https://www.reddit.com/r/fematika Code : https://github.com/Fematika/Animations Notes : None yet
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
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?
Topological Spaces: The Subspace Topology
Today, we discuss the subspace topology, which is a useful tool to construct new topologies.
From playlist Topology & Manifolds
Classical and Digital Topological Groups
A research talk presented at the Fairfield University Mathematics Research Seminar, October 6, 2022. Should be accessible to a general mathematics audience, combining ideas from topology, graph theory, and abstract algebra. The paper is by me and Dae Woong Lee, available here: https://arx
From playlist Research & conference talks
What is a Manifold? Lesson 4: Countability and Continuity
In this lesson we review the idea of first and second countability. Also, we study the topological definition of a continuous function and then define a homeomorphism.
From playlist What is a Manifold?
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]🔥
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?
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 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?
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
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
Topological Spaces: The Standard Topology on R^n
Today, we construct the standard topology, which gives us the way we usually think about R^n.
From playlist Topology & Manifolds