Set-theoretic topology
In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independent of Zermelo–Fraenkel set theory (ZFC). (Wikipedia).
In mathematics, set-theoretic topology is a subject that combines set theory and general topology. It focuses on topological questions that are independent of Zermelo–Fraenkel set theory (ZFC). (Wikipedia).
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
Introduction to Set Theory (Discrete Mathematics)
Introduction to Set Theory (Discrete Mathematics) This is a basic introduction to set theory starting from the very beginning. This is typically found near the beginning of a discrete mathematics course in college or at the beginning of other advanced mathematics courses. ***************
From playlist Set Theory
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
Introduction to sets || Set theory Overview - Part 2
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
Set Theory (Part 3): Ordered Pairs and Cartesian Products
Please feel free to leave comments/questions on the video and practice problems below! In this video, I cover the Kuratowski definition of ordered pairs in terms of sets. This will allow us to speak of relations and functions in terms of sets as the basic mathematical objects and will ser
From playlist Set Theory by Mathoma
Introduction to sets || Set theory Overview - Part 1
A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other #sets. The #set with no element is the empty
From playlist Set Theory
We give some basic definitions and notions associated with sets. In particular, we describe sets via the "roster method", via a verbal description, and with set-builder notation. We also give an example of proving the equality of two sets. Please Subscribe: https://www.youtube.com/michael
From playlist Proof Writing
Introduction to Sets and Set Notation
This video defines a set, special sets, and set notation.
From playlist Sets (Discrete Math)
Set Theory (Part 2): ZFC Axioms
Please feel free to leave comments/questions on the video and practice problems below! In this video, I introduce some common axioms in set theory using the Zermelo-Fraenkel w/ choice (ZFC) system. Five out of nine ZFC axioms are covered and the remaining four will be introduced in their
From playlist Set Theory by Mathoma
MathZero, The Classification Problem, and Set-Theoretic Type Theory - David McAllester
Seminar on Theoretical Machine Learning Topic: MathZero, The Classification Problem, and Set-Theoretic Type Theory Speaker: David McAllester Affiliation: Toyota Technological Institute at Chicago Date: May 14, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Geometric Representation of Structured Extensions in Ergodic Theory - Henrik Kreidler
Special Year Research Seminar Topic: Geometric Representation of Structured Extensions in Ergodic Theory Speaker: Henrik Kreidler Affiliation: Bergische Universität Wuppertal Date: March 14, 2023 The Mackey-Zimmer representation theorem is a key structural result from ergodic theory: Eve
From playlist Mathematics
Duality in Higher Categories-I by Pranav Pandit
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)
Elchanan Solomon (08/25/21): Dimensionality Reduction via Distributed Persistence: DIPOLE
Title: Dimensionality Reduction via Distributed Persistence: DIPOLE Abstract: We propose a new gradient-descent-based paradigm for dimensionality reduction, called DIPOLE, consisting of a loss function with two terms: a local metric term that forces the projection to be an isometry on sm
From playlist AATRN 2021
Henry Adams (6/2/20): From persistent homology to machine learning
Title: From persistent homology to machine learning Abstract: I will give an overview of a variety of ways to turn persistent homology output into input for machine learning tasks, including a discussion of the stability and interpretability properties of these methods. Persistent homolog
From playlist SIAM Topological Image Analysis 2020
Wolfram Physics Project: Working Session Tuesday, Nov. 2, 2021 [Topos Theory]
This is a Wolfram Physics Project working session about Topos Theory in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/
From playlist Wolfram Physics Project Livestream Archive
An Amazing Connection Between the Riemann Hypothesis and Topology
https://gregoriousmaths.com/2021/08/19/a-couple-of-other-connections-between-number-theory-and-topology/ 0:00 Introduction and plan 2:32 The Riemann hypothesis 7:22 Introducing the complex we will study 19:41 Studying the asymptotic behaviour of \beta_k(\Delta_n) 22:54 Some number theoret
From playlist Summer of Math Exposition Youtube Videos
Yuichi Ike (6/29/22): RipsNet: fast and robust estimation of persistent homology for point clouds
I will talk about the data-driven approach to estimating persistence diagrams (PDs) of point clouds. In the practical use of persistent homology, there are two major limitations: the computational complexity of computing PDs exactly and their sensitivity to even low-level proportions of ou
From playlist AATRN 2022
How Proteins Get Where They’re Supposed to Go in Cells - T. Miller - 5/11/2016
Entire title - "Signed, Sealed, Delivered: How Proteins Get Where They’re Supposed to Go in Cells" by Thomas Miller, Professor of Chemistry, Caltech. Learn more about: - Miller Group: http://millergroup.caltech.edu/Miller_Group/Home.html - Watson Lecture Series: https://www.caltech.edu/ma
From playlist Research & Science
Markus Haase : On some operator-theoretic aspects of ergodic theory
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Dynamical Systems and Ordinary Differential Equations
This video is about topological spaces and some of their basic properties.
From playlist Basics: Topology