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)
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 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
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
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)
Every Compact Set in n space is Bounded
Every Compact Set in n space is Bounded If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Advanced Calculus
Every Closed Subset of a Compact Space is Compact Proof
Every Closed Subset of a Compact Space is Compact Proof If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Topology
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
This video is about compactness and some of its basic properties.
From playlist Basics: Topology
Dustin Clausen - Toposes generated by compact projectives, and the example of condensed sets
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ The simplest kind of Grothendieck topology is the one with only trivial covering sieves, where the associated topos is equal to the presheaf topos. The next simplest topology ha
From playlist Toposes online
Dustin Clausen: New foundations for functional analysis
Talk by Dustin Clausen in Global Noncommutative Geometry Seminar (Americas) on November 12, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Locally Cartesian Closed Infinity Categories - Joachim Kock
Joachim Kock Universitat Autonoma de Barcelona February 21, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Holomorphic Floer theory and the Fueter equation - Aleksander Doan
Joint IAS/Princeton University Symplectic Geometry Seminar Holomorphic Floer theory and the Fueter equation Aleksander Doan Columbia University Date: April 25, 2022 I will discuss an idea of constructing a category associated with a pair of holomorphic Lagrangians in a hyperkahler manif
From playlist Mathematics
Sergey Melikhov, Steklov Math Institute (Moscow) Title: Fine Shape Abstract: A shape theory is something which is supposed to agree with homotopy theory on polyhedra and to treat more general spaces by looking at their polyhedral approximations. Or if you prefer, it is something which is s
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
Lecture 6: HKR and the cotangent complex
In this video, we discuss the cotangent complex and give a proof of the HKR theorem (in its affine version) Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://www.uni-m
From playlist Topological Cyclic Homology
Categorical non-properness in wrapped Floer theory - Sheel Ganatra
Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Categorical non-properness in wrapped Floer theory Speaker: Sheel Ganatra Affiliation: University of Southern California Date: April 02, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Virtual rigid motives of definable sets in valued fields - A. Forey - Workshop 2 - CEB T1 2018
Arthur Forey (Sorbonne Université) / 08.03.2018 Virtual rigid motives of definable sets in valued fields. In an instance of motivic integration, Hrushovski and Kazhdan study the definable sets in the theory of algebraically closed valued fields of characteristic zero. They show that the
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Generation criteria for the Fukaya category II - Mohammed Abouzaid
Mohammed Abouzaid MIT May 12, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
All About Closed Sets and Closures of Sets (and Clopen Sets) | Real Analysis
We introduced closed sets and clopen sets. We'll visit two definitions of closed sets. First, a set is closed if it is the complement of some open set, and second, a set is closed if it contains all of its limit points. We see examples of sets both closed and open (called "clopen sets") an
From playlist Real Analysis
Oscar Randal Williams: Moduli spaces of manifolds (part 3)
The lecture was held within the framework of the Hausdorff Trimester Program: Homotopy theory, manifolds, and field theories and Introductory School (05.05.2015)
From playlist HIM Lectures 2015