Separation axioms | Topology | Properties of topological spaces

Regular space

In topology and related fields of mathematics, a topological space X is called a regular space if every closed subset C of X and a point p not contained in C admit non-overlapping open neighborhoods. Thus p and C can be separated by neighborhoods. This condition is known as Axiom T3. The term "T3 space" usually means "a regular Hausdorff space". These conditions are examples of separation axioms. (Wikipedia).

Regular space
Video thumbnail

What is space?

What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:

From playlist Science Unplugged: Physics

Video thumbnail

What is spacetime?

"Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu"

From playlist Science Unplugged: Special Relativity

Video thumbnail

Dual Space

Dual spaces and linear functionals In this video, I introduce the concept of a dual space, which is the analog of a "shadow world" version, but for vector spaces. I also give some examples of linear and non-linear functionals. This seems like an innocent topic, but it has a huge number of

From playlist Dual Spaces

Video thumbnail

Metric spaces -- Proofs

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

Video thumbnail

Worldwide Calculus: Euclidean Space

Lecture on 'Euclidean Space' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.

From playlist Multivariable Spaces and Functions

Video thumbnail

What is a metric space ?

Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener

From playlist Topology

Video thumbnail

What Is Nothing?

Is there any place in the Universe where there's truly nothing? Consider the gaps between stars and galaxies? Or the gaps between atoms? What are the properties of nothing?

From playlist Guide to Space

Video thumbnail

Complete metric space: example & proof

This video discusses an example of particular metric space that is complete. The completeness is proved with details provided. Such ideas are seen in branches of analysis.

From playlist Mathematical analysis and applications

Video thumbnail

Fooling intersections of low-weight halfspaces - Rocco Servedio

Computer Science/Discrete Mathematics Seminar I Topic: Fooling intersections of low-weight halfspaces Speaker: Rocco Servedio Affiliation: Columbia University Date: October 30, 2017 For more videos, please visit http://video.ias.edu

From playlist Mathematics

Video thumbnail

Cornelia Schneider: Regularity in Besov spaces of parabolic PDEs

HYBRID EVENT This talk is concerned with the regularity of solutions to parabolic evolution equations. Special attention is paid to the smoothness in the specific scales $\ B^{r}_{\tau,\tau}, \ \frac{1}{\tau}=\frac{r}{d}+\frac{1}{p}\ $ of Besov spaces. The regularity in these spaces deter

From playlist Analysis and its Applications

Video thumbnail

Philippe G LeFloch - Weakly regular spacetimes with T2 symmetry

I will discuss the initial value problem for the Einstein equations and present results concerning the existence and asymptotic behavior of spacetimes, when the initial data set is assumed to be T2 symmetric and satisfies weak regularity conditions so that the spacetimes may exhibit impul

From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale

Video thumbnail

Jarosław Buczyński (6/29/17) Bedlewo: Constructions of k-regular maps using finite local schemes

A continuous map R^m → R^N or C^m → C^N is called k-regular if the images of any k distinct points are linearly independent. Given integers m and k a problem going back to Chebyshev and Borsuk is to determine the minimal value of N for which such maps exist. The methods of algebraic topolo

From playlist Applied Topology in Będlewo 2017

Video thumbnail

Commutative algebra 60: Regular local rings

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. We define regular local rings as the local rings whose dimension is equal to the dimension of their cotangent space. We give s

From playlist Commutative algebra

Video thumbnail

algebraic geometry 24 Regular functions

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers regular functions on affine and quasiprojective varieties.

From playlist Algebraic geometry I: Varieties

Video thumbnail

Nicolas Perkowski: Lecture #2

This is the second lecture on "A Markovian perspective on some singular SPDEs" taught by Professor Nicolas Perkowski. For more materials and slides visit: https://sites.google.com/view/oneworld-pderandom/home

From playlist Summer School on PDE & Randomness

Video thumbnail

Martin Hairer Mini-course 2: Introduction to Regularity Structures

SMRI-MATRIX Symposium with Martin Hairer 18 February 2021: Mini-course 2 Title: Introduction to Regularity Structures Part 2 Symposium website: https://sites.google.com/monash.edu/symposium-with-martin-hairer/home Question from audience member (1:01:26): Is it possible to encode non-l

From playlist Symposium with Martin Hairer

Video thumbnail

What is a Vector Space?

What is a Vector Space? Definition of a Vector space.

From playlist Linear Algebra

Related pages

Topological space | Separated sets | Topology | Clopen set | Theorem | T1 space | Mathematical analysis | Base (topology) | Disjoint sets | Pseudonormal space | Hausdorff space | Counterexample | Semiregular space | Urysohn and completely Hausdorff spaces | Point (geometry) | Mathematics | Zero-dimensional space | Subset | Interior (topology) | Kolmogorov space | History of the separation axioms | Regular open set | Normal space | Separation axiom | Closed set