In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology). (Wikipedia).
Topological Spaces: The Subspace Topology
Today, we discuss the subspace topology, which is a useful tool to construct new topologies.
From playlist Topology & Manifolds
The Subspace Topology is a Topology Proof
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Subspace Topology is a Topology Proof
From playlist Proofs
Finding the Subspace Topology Easy Example
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Finding the Subspace Topology Easy Example
From playlist Topology
Classic linear algebra exercise: the union of a subspace is a subspace if and only if one is contained in the other. This is also good practice with the definition of a subspace, and also shows how to prove statements of the form p implies (q or r) Check out my vector space playlist: http
From playlist Vector Spaces
Linear Algebra: What is a Subspace?
Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/
From playlist Basics: Linear Algebra
Subspaces of a vector space. Sums and direct sums.
From playlist Linear Algebra Done Right
A matrix of coefficients, when viewed in column form, is used to create a column space. This is simply the space created by a linear combination of the column vectors. A resulting vector, b, that does not lie in this space will not result in a solution to the linear system. A set of vec
From playlist Introducing linear algebra
What's a subspace of a vector space? How do we check if a subset is a subspace?
From playlist Linear Algebra
This video is about connectedness and some of its basic properties.
From playlist Basics: Topology
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?
Introduction to Homotopy Theory- PART 1: UNIVERSAL CONSTRUCTIONS
The goal of this series is to develop homotopy theory from a categorical perspective, alongside the theory of model categories. We do this with the hope of eventually developing stable homotopy theory, a personal goal a passion of mine. I'm going to follow nLab's notes, but I hope to add t
From playlist Introduction to Homotopy Theory
AlgTop1: One-dimensional objects
This is the first lecture of this beginner's course in Algebraic Topology (after the Introduction). In it we introduce the two basic one-dimensional objects: the line and circle. The latter has quite a few different manifestations: as a usual Euclidean circle, as the projective line of one
From playlist Algebraic Topology: a beginner's course - N J Wildberger
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
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
Enrique Macias-Virgo (5/27/21): Homotopic distance and Generalized motion planning
Lusternik-Schnirelmann category and topological complexity are particular cases of a more general notion, that we call homotopic distance between two maps. As a consequence, several properties of those invariants can be proved in a unified way and new results arise. For instance, we prove
From playlist Topological Complexity Seminar
Topology PhD Qualifying Exam Problems (Stream 1)
Just practicing some arguments from topology qualifying exam problems. A few folks said they wanted me to hang out here instead of on Twitch today. 00:00:00 Dead Air 00:00:53 I exist huzzah! 00:09:26 Continuous Images of Metric Spaces in Hausdorff Spaces Problem 01:13:45 Separable First C
From playlist CHALK Streams
Kolchin: Irreducibility = Has Deformations for Sober Topological Spaces
This is the key lemma we want to apply to prove irreducibility theorems. This is based of what is done in a paper of Ishii and Kollar and is the basis of something I have done with with Lance and James.
From playlist Kolchin Irreducibility
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