In this video, I discuss the finite intersection property, which is a nice generalization of the Cantor Intersection Theorem and a very elegant application of compactness. Enjoy this topology-filled adventure! Compactness: https://youtu.be/xiWizwjpt8o Cantor Intersection Theorem: https:/
From playlist Topology
Infinite Intersection of Open Sets that is Closed Proof
Infinite Intersection of Open Sets that is Closed 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 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 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)
This video is about compactness and some of its basic properties.
From playlist Basics: 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
Lecture 21 (w/J. Sands!): Intersections and Unions of Indexed Families of Sets (+Arch Property)
course page: https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html handouts - DZB, Emory videography - Eric Melton, UVM
From playlist Fundamentals of Mathematics
Here is a wonderful theorem about the intersection of decreasing closed sets, called the Cantor Intersection Theorem, also known as the Finite Intersection Property. Enjoy! Topology Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmA13vj9xkHGGBXRMV32EKVI Subscribe to my channel:
From playlist Topology
Fundamentals of Mathematics - Lecture 33: Dedekind's Definition of Infinite Sets are FInite Sets
https://www.uvm.edu/~tdupuy/logic/Math52-Fall2017.html
From playlist Fundamentals of Mathematics
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)
Lecture 8: Lebesgue Measurable Subsets and Measure
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=cqdUuREzGuo&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Stable and NIP regularity in groups - G. Conant - Workshop 1 - CEB T1 2018
Gabriel Conant (Notre Dame) / 01.02.2018 We use local stability theory to prove a group version of Szemer´edi regularity for stable subsets of finite groups. Toward generalizing this result to the NIP setting, we consider definable set systems of finite VC-dimension in pseudofinite groups
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=OHiu2F18dFA&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Parvaneh Joharinad (7/27/22): Curvature of data
Abstract: How can one determine the curvature of data and how does it help to derive the salient structural features of a data set? After determining the appropriate model to represent data, the next step is to derive the salient structural features of data based on the tools available for
From playlist Applied Geometry for Data Sciences 2022
Plenary lecture 6 by Mladen Bestvina
Geometry Topology and Dynamics in Negative Curvature URL: https://www.icts.res.in/program/gtdnc DATES: Monday 02 Aug, 2010 - Saturday 07 Aug, 2010 VENUE : Raman Research Institute, Bangalore DESCRIPTION: This is An ICM Satellite Conference. The conference intends to bring together ma
From playlist Geometry Topology and Dynamics in Negative Curvature
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