Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
This video is about compactness and some of its basic properties.
From playlist Basics: Topology
Math 131 092816 Continuity; Continuity and Compactness
Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 131 092116 Properties of Compact Sets
Properties of compact sets. Compact implies closed; closed subsets of compact sets are compact; collections of compact sets that satisfy the finite intersection property have a nonempty intersection; infinite subsets of compact sets must have a limit point; the infinite intersection of ne
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 101 Introduction to Analysis 113015: Compact Sets, ct'd
Compact sets, continued. Recalling various facts about compact sets. Compact implies infinite subsets have limit points (accumulation points), that is, compactness implies limit point compactness; collections of compact sets with the finite intersection property have nonempty intersectio
From playlist Course 6: Introduction to Analysis
Math 131 Fall 2018 100318 Heine Borel Theorem
Definition of limit point compactness. Compact implies limit point compact. A nested sequence of closed intervals has a nonempty intersection. k-cells are compact. Heine-Borel Theorem: in Euclidean space, compactness, limit point compactness, and being closed and bounded are equivalent
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Math 101 Introduction to Analysis 112515: Introduction to Compact Sets
Introduction to Compact Sets: open covers; examples of finite and infinite open covers; definition of compactness; example of a non-compact set; compact implies closed; closed subset of compact set is compact; continuous image of a compact set is compact
From playlist Course 6: Introduction to Analysis
Math 131 Fall 2018 100118 Properties of Compact Sets
Review of compactness. Properties: compactness is not relative. Compact implies closed. Closed subset of compact set is compact. [Infinite] Collection of compact sets with finite intersection property has a nonempty intersection.
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
MAST30026 Lecture 8: Compactness I
This is the first of several lectures on compactness. I recalled the proof of the Bolzano-Weierstrass theorem, defined sequential compactness in metric spaces and the characterisation of continuity of functions in terms of limits, and proved that the image of a compact set is compact. Lec
From playlist MAST30026 Metric and Hilbert spaces
Markus Haase : Operators in ergodic theory - Lecture 3 : Compact semigroups and splitting theorems
Abstract : The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems Recording during the thematic meeting : "Probabilistic Aspects of Multiple Ergodic Averages " the December 8
From playlist Dynamical Systems and Ordinary Differential Equations
Introduction to Scalar Curvature and Convergence - Christina Sormani
Emerging Topics Working Group Topic: Introduction to Scalar Curvature and Convergence Speaker: Christina Sormani Affilaition: IAS Date: October 15, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Real Analysis - Part 14 - Heine-Borel theorem [dark versio]
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From playlist Real Analysis [dark version]
Jordan Sahattchieve: A Fibering Theorem for 3-Manifolds
Jordan Sahattchieve Title: A Fibering Theorem for 3-Manifolds In this talk, I will endeavor to communicate a new fibering theorem for 3-manifolds in the style of Stalling's Fibration Theorem.
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Math 101 Fall 2017 120117 Compact Sets: The Heine-Borel Theorem
Theorem: the continuous image of a compact set is compact. Theorem: a collection of compact sets satisfying the finite intersection property has a non-empty intersection. Theorem: In R, closed and bounded intervals are compact. Corollary: Heine-Borel theorem (in R, a set is compact iff
From playlist Course 6: Introduction to Analysis (Fall 2017)
Real Analysis Ep 27: Extreme value theorem
Episode 27 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is even more about the extreme value theorem, and a bit about uniform continuity. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/
From playlist Math 3371 (Real analysis) Fall 2020
Matthew Kennedy: Noncommutative convexity
Talk by Matthew Kennedy in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on May 5, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri (L4) by Sunil Mukhi
Seminar Lecture Series - Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri Speaker: Sunil Mukhi (IISER Pune) Date : Mon, 20 March 2023 to Fri, 21 April 2023 Venue: Online (Zoom & Youtube) ICTS is pleased to announce special lecture series by Prof. Sunil Mukh
From playlist Lecture Series- Advanced General Relativity: A Centennial Tribute to Amal Kumar Raychaudhuri -2023
Mathematical Research Lecture -- Kyle Broder -- Curvature and Moduli
A recent talk I gave concerning the link between the curvature of the total space of a family of compact complex manifolds and the moduli-theoretic behaviour of the fibres. Part of this research appears in my Ph.D. thesis, and will appear in an upcoming preprint. 💪🙏 Support the channel b
From playlist Research Lectures
Compact sets enjoy some mysterious properties, which I'll discuss in this video. More precisely, compact sets are always bounded and closed. The beauty of this result lies in the proof, which is an elegant application of this subtle concept. Enjoy! Compactness Definition: https://youtu.be
From playlist Topology
Koen van den Dungen: Localisations and the Kasparov product in unbounded KK-theory
Talk by Koen van den Dungen in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on May 19, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)