General topology | Topological spaces | Topology

Discrete space

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous sequence, meaning they are isolated from each other in a certain sense. The discrete topology is the finest topology that can be given on a set. Every subset is open in the discrete topology so that in particular, every singleton subset is an open set in the discrete topology. (Wikipedia).

Video thumbnail

What is Discrete Mathematics?

This video explains what is taught in discrete mathematics.

From playlist Mathematical Statements (Discrete Math)

Video thumbnail

Discrete Structures, Oct 20: Counting

Combinations, Permutations, Pigeonhole Principle

From playlist Discrete Structures

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

Introduction to Discrete and Continuous Functions

This video defines and provides examples of discrete and continuous functions.

From playlist Introduction to Functions: Function Basics

Video thumbnail

Vector spaces and subspaces

After our introduction to matrices and vectors and our first deeper dive into matrices, it is time for us to start the deeper dive into vectors. Vector spaces can be vectors, matrices, and even function. In this video I talk about vector spaces, subspaces, and the porperties of vector sp

From playlist Introducing linear algebra

Video thumbnail

Discrete Math - 9.3.1 Matrix Representations of Relations and Properties

How to represent a relation using a matrix and easy tips for determining if the relation is reflexive, irreflexive, symmetric, antisymetric, asymmetric and transitive. Matrix operations are also reviewed (meet, join and Boolean product). Textbook: Rosen, Discrete Mathematics and Its Appl

From playlist Discrete Math I (Entire Course)

Video thumbnail

Formal Definition of a Function using the Cartesian Product

Learning Objectives: In this video we give a formal definition of a function, one of the most foundation concepts in mathematics. We build this definition out of set theory. **************************************************** YOUR TURN! Learning math requires more than just watching vid

From playlist Discrete Math (Full Course: Sets, Logic, Proofs, Probability, Graph Theory, etc)

Video thumbnail

What is a Vector Space?

This video explains the definition of a vector space and provides examples of vector spaces.

From playlist Vector Spaces

Video thumbnail

Understand Vector-Quantized Variational Autoencoder (VQ-VAE) for Image Generation #stablediffusion

Vector-Quantized Variational Autoencoder (VQ-VAE) for Image Generation explained in Detail. The main component of DALL-E of 2020. On the road to DIFFUSION for text-to-video. Generative AI. 3 videos before this video: https://youtu.be/onuIy6PC1ic https://youtu.be/BHzU-jq-AcM https://youtu.

From playlist Stable Diffusion / Latent Diffusion models for Text-to-Image AI

Video thumbnail

Lecture 11: Discrete Curves (Discrete Differential Geometry)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg

From playlist Discrete Differential Geometry - CMU 15-458/858

Video thumbnail

Alex Margolis: Quasi-actions and almost normal subgroups

CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 27, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM

From playlist Virtual Conference

Video thumbnail

Alex Margolis: Quasi-actions and almost normal subgroups

CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 27, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM

From playlist VIRTUAL EVENT GEOMETRIC GROUP THEORY CONFERENCE

Video thumbnail

Konrad Polthier (7/27/22): Boundary-sensitive Hodge decompositions

Abstract: We provide a theoretical framework for discrete Hodge-type decomposition theorems of piecewise constant vector fields on simplicial surfaces with boundary that is structurally consistent with decomposition results for differential forms on smooth manifolds with boundary. In parti

From playlist Applied Geometry for Data Sciences 2022

Video thumbnail

Jan Maas : Gradient flows and Ricci cuevature in discrete and quantum probability

Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the August 28, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent

From playlist Geometry

Video thumbnail

Lecture 19 | The Fourier Transforms and its Applications

Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood demonstrates aliasing by showing the class what happens when you under sample music. The Fourier transform is a tool for solving physical probl

From playlist Lecture Collection | The Fourier Transforms and Its Applications

Video thumbnail

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group

Lie Groups and Lie Algebras: Lesson 39 - The Universal Covering Group We are finally in position to understand the nature of the Universal Covering Group and its connection to all the Lie groups which share a single Lie algebra. This is a critical lecture! In this lecture we simply state

From playlist Lie Groups and Lie Algebras

Video thumbnail

History of Science and Technology Q&A (March 9, 2022)

Stephen Wolfram hosts a live and unscripted Ask Me Anything about the history of science and technology for all ages. Find the playlist of Q&A's here: https://wolfr.am/youtube-sw-qa Originally livestreamed at: https://twitch.tv/stephen_wolfram If you missed the original livestream of

From playlist Stephen Wolfram Ask Me Anything About Science & Technology

Video thumbnail

Introduction to Metric Spaces

Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric

From playlist Topology

Video thumbnail

Lecture 14: Discrete Surfaces (Discrete Differential Geometry)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg

From playlist Discrete Differential Geometry - CMU 15-458/858

Related pages

Cantor space | Topological space | Metric space | Lie group | Pontryagin duality | Accumulation point | Countable set | Counterexamples in Topology | If and only if | Finite set | Continued fraction | Isolated point | Topology | Ultrafilter (set theory) | Free object | Topological group | First-countable space | Group (mathematics) | Comparison of topologies | Discrete group | Boolean prime ideal theorem | Domain of a function | Euclidean topology | Foundations of mathematics | Second-countable space | Empty set | Logical disjunction | Hausdorff space | Mathematical structure | Uniform space | Taxicab geometry | Ternary numeral system | Cylinder set | Open set | Natural number | Set (mathematics) | Totally bounded space | Locally constant function | Singleton (mathematics) | Category theory | Subset | Morphism | Compact space | Manifold | Trivial topology | List of topologies | Fiber (mathematics) | Irrational number | Subspace topology | Logical conjunction | Cardinality | Cantor set | Product topology | Closed set