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 1.3 : 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
Topological Spaces: The Subspace Topology
Today, we discuss the subspace topology, which is a useful tool to construct new topologies.
From playlist Topology & Manifolds
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
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
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]🔥
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
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
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
Lie Groups and Lie Algebras: Lesson 36 - Review of continuity and homeomorphisms
Lie Groups and Lie Algebras: Lesson 36 - Review of continuity and homeomorphisms This is a review lesson regarding the topological definition of continuity, homeomorphism, and topological properties. This is important because the Fundamental group of a topological space is a topological
From playlist Lie Groups and Lie Algebras
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
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
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
Said Hamoun (2/23/23): On the rational topological complexity of coformal elliptic spaces
We establish some upper and lower bounds of the rational topological complexity for certain classes of elliptic spaces. Our techniques permit us in particular to show that the rational topological complexity coincides with the dimension of the rational homotopy for some special families of
From playlist Topological Complexity Seminar
Uri Bader - 1/4 Algebraic Representations of Ergodic Actions
Ergodic Theory is a powerful tool in the study of linear groups. When trying to crystallize its role, emerges the theory of AREAs, that is Algebraic Representations of Ergodic Actions, which provides a categorical framework for various previously studied concepts and methods. Roughly, this
From playlist Uri Bader - Algebraic Representations of Ergodic Actions
MAST30026 Lecture 19: Duality and Hilbert space
I began by proving the universal property of the completion of a normed space. I then discussed characterisations of finite-dimensionality for vector spaces, introduced the continuous linear dual for normed spaces and the operator norm, and stated the duality theorem or L^p spaces which sa
From playlist MAST30026 Metric and Hilbert spaces
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
Yuzhou Chen (10/27/21): Topological Relational Learning on Graphs
Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these challenges, we propose a novel topological neural framewo
From playlist AATRN 2021
In this video, I introduce the order topology and prove that it is Hausdorff. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Topology