Algebraic Topology - 1 - Compact Hausdorff Spaces (a Review of Point-Set Topology)
This is mostly a review point set topology. In general it is not true that a bijective continuous map is invertible (you need to worry about the inverse being continuous). In the case that your spaces are compact hausdorff this is true! We prove this in this video and review necessary fac
From playlist Algebraic Topology
Hausdorff Example 1: Cofinite Topology
Point Set Topology: We recall the notion of a Hausdorff space and consider the cofinite topology as a source of non-Hausdorff examples. We also note that this topology is always compact.
From playlist Point Set Topology
Hausdorff Example 3: Function Spaces
Point Set Topology: For a third example, we consider function spaces. We begin with the space of continuous functions on [0,1]. As a metric space, this example is Hausdorff, but not complete. We consider Cauchy sequences and a possible completion.
From playlist Point Set Topology
Yoshihiro Ohnita: Minimal Maslov number of R-spaces canonically embedded in Einstein-Kähler C-spaces
An R-space is a compact homogeneous space obtained as an orbit of the isotropy representation of a Riemannian symmetric space. It is known that each R-space has the canonical embedding into a Kähler C-space as a real form which is a compact embedded totally geodesic Lagrangian submanifold.
From playlist Geometry
MAST30026 Lecture 11: Hausdorff spaces (Part 1)
I introduced the Hausdorff condition, proved some basic properties, discussed the "real line with a double point" as an example of a non-Hausdorff space, proved that a compact subspace of a Hausdorff space is closed, and that continuous bijections from compact to Hausdorff spaces are homeo
From playlist MAST30026 Metric and Hilbert spaces
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
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)
An introduction to the Gromov-Hausdorff distance
Title: An introduction to the Gromov-Hausdorff distance Abstract: We give a brief introduction to the Hausdorff and Gromov-Hausdorff distances between metric spaces. The Hausdorff distance is defined on two subsets of a common metric space. The Gromov-Hausdorff distance is defined on any
From playlist Tutorials
This video is about compactness and some of its basic properties.
From playlist Basics: Topology
Dennis Gaitsgory - Tamagawa Numbers and Nonabelian Poincare Duality, II [2013]
Dennis Gaitsgory Wednesday, August 28 4:30PM Tamagawa Numbers and Nonabelian Poincare Duality, II Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Abstract: This will be a continuation of Jacob Lurie’s talk. Let X be an al
From playlist Number Theory
Convex Integration Applied to Fluid Dynamics by Helena Nussenzveig Lopes
PROGRAM TURBULENCE: PROBLEMS AT THE INTERFACE OF MATHEMATICS AND PHYSICS ORGANIZERS Uriel Frisch (Observatoire de la Côte d'Azur and CNRS, France), Konstantin Khanin (University of Toronto, Canada) and Rahul Pandit (IISc, India) DATE & TIME 16 January 2023 to 27 January 2023 VENUE Ramanuj
From playlist Turbulence: Problems at the Interface of Mathematics and Physics 2023
Martina Hofmanová: Solvability and ill posedness of the isentropic Euler system
The lecture was held within the of the Hausdorff Junior Trimester Program: Randomness, PDEs and Nonlinear Fluctuations. Abstract: I will discuss several puzzling results related to solvability and ill-posedness of the isentropic Euler system. On the one hand, the method of convex integrat
From playlist HIM Lectures: Junior Trimester Program "Randomness, PDEs and Nonlinear Fluctuations"
ITHT: Part 12- Model Structure on Topological Spaces
Credits: nLab: https://ncatlab.org/nlab/show/Introduction+to+Homotopy+Theory#TheClassicalModelStructureOfTopologicalSpaces Animation library: https://github.com/3b1b/manim My own code/modified library: https://github.com/treemcgee42/youtub...
From playlist Introduction to Homotopy Theory
Sequential Spectra- Part 5: Spectrification
The second part of the Omega spectra section on nLab. Credits: nLab: https://ncatlab.org/nlab/show/Introdu... Animation library: https://github.com/3b1b/manim Music: ► Artist Attribution • Music By: "KaizanBlu" • Track Name: "Remember (Extended Mix)" • YouTube Track Link: https://bi
From playlist Sequential Spectra
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
Hausdorff School: Lecture by László Székelyhidi
Inauguration of the Hausdorff School The “Hausdorff School for Advanced Studies in Mathematics” is an innovative new program for postdocs by the Hausdorff Center. The official inauguration took place on October 20, 2015. Lecture by László Székelyhidi on "The h-principle in fluid mechanic
From playlist Inauguration of Hausdorff School 2015
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
Hans Feichtinger: Fourier Analysis via the Banach Gelfand Triple
The lecture was held within the framework of the Hausdorff Trimester Program Mathematics of Signal Processing. In this MATLAB-based presentation the author will explain how one can understand and illustrate the foundations of Gabor analysis with the help of MATLAB. From the point of view
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
AlgTopReview4: Free abelian groups and non-commutative groups
Free abelian groups play an important role in algebraic topology. These are groups modelled on the additive group of integers Z, and their theory is analogous to the theory of vector spaces. We state the Fundamental Theorem of Finitely Generated Commutative Groups, which says that any such
From playlist Algebraic Topology