Metric space definition and examples. Welcome to the beautiful world of topology and analysis! In this video, I present the important concept of a metric space, and give 10 examples. The idea of a metric space is to generalize the concept of absolute values and distances to sets more gener
From playlist Topology
What is a metric space? An example
This is a basic introduction to the idea of a metric space. I introduce the idea of a metric and a metric space framed within the context of R^n. I show that a particular distance function satisfies the conditions of being a metric.
From playlist Mathematical analysis and applications
Introduction to Metric Spaces - Definition of a Metric. - The metric on R - The Euclidean Metric on R^n - A metric on the set of all bounded functions - The discrete metric
From playlist Topology
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Introduction to Geometer's Sketchpad: Measurements
This video demonstrates some of the measurement and calculation features of Geometer's Sketchpad.
From playlist Geometer's Sketchpad
Weird notions of "distance" || Intro to Metric Spaces
Visit https://brilliant.org/TreforBazett/ to get started learning STEM for free, and the first 200 people will get 20% off their annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Weird, fun
From playlist Cool Math Series
Metric Conversion Shortcut (Single Digit)
#shorts This video shows a shortcut for performing metric unit conversion with a given single digit. https://mathispower4u.com
From playlist Math Shorts
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
Ex: Metric Conversions Using Unit Fractions - Length
This video provides three examples of how to perform metric conversions involving length using unit fractions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Unit Conversions: Metric Units
Guido Montúfar : Fisher information metric of the conditional probability politopes
Recording during the thematic meeting : "Geometrical and Topological Structures of Information" the September 01, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent
From playlist Geometry
Lipschitz rigidity for scalar curvature - Bernhard Hanke
Analysis & Mathematical Physics Topic: Lipschitz rigidity for scalar curvature Speaker: Bernhard Hanke Affiliation: University of Augsburg, Member, School of Mathematics Date: October 05, 2022 Lower scalar curvature bounds on spin Riemannian manifolds exhibit remarkable rigidity properti
From playlist Mathematics
Harmonic Maps between surfaces and Teichmuller theory (Lecture - 1) by Michael Wolf
Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b
From playlist Geometry, Groups and Dynamics (GGD) - 2017
Johnathan Bush (11/5/21): Maps of Čech and Vietoris–Rips complexes into euclidean spaces
We say a continuous injective map from a topological space to k-dimensional euclidean space is simplex-preserving if the image of each set of at most k+1 distinct points is affinely independent. We will describe how simplex-preserving maps can be useful in the study of Čech and Vietoris–Ri
From playlist Vietoris-Rips Seminar
Stefan Wenger - 21 September 2016
Wenger, Stefan "“Plateau’s problem in metric spaces and applications”"
From playlist A Mathematical Tribute to Ennio De Giorgi
Henry Adams (10/11/17): Metric reconstruction via optimal transport
Given a sample of points X in a metric space M and a scale parameter r, the Vietoris-Rips simplicial complex VR(X;r) is a standard construction to attempt to recover M from X up to homotopy type. A deficiency of this approach is that VR(X;r) is not metrizable if it is not locally finite, a
From playlist AATRN 2017
D. Stern - Harmonic map methods in spectral geometry (version temporaire)
Over the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to connections to the study of sphere-valued harmonic maps and minimal immersions. In this talk, I'll
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Johannes Ebert - Rigidity theorems for the diffeomorphism action on spaces of metrics of (...)
The diffeomorphism group $\mathrm{Diff}(M)$ of a closed manifold acts on the space $\mathcal{R}^+ (M)$ of positive scalar curvature metrics. For a basepoint $g$, we obtain an orbit map $\sigma_g: \mathrm{Diff}(M) \to \mathcal{R}^ (M)$ which induces a map $(\sigma_g)_*:\pi_*( \mathrm{Diff}(
From playlist Not Only Scalar Curvature Seminar
Regularity of the limit set of embedded Poincaré Disks - Vincent Borelli
Workshop on the h-principle and beyond Topic: Regularity of the limit set of embedded Poincaré Disks Speaker: Vincent Borelli Affiliation: University of Lyon Date: November 4, 2021 Abstract: Let f be an embedding of a non compact manifold into an Euclidean space and p_n be a divergent se
From playlist Mathematics
D. Stern - Harmonic map methods in spectral geometry
Over the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to connections to the study of sphere-valued harmonic maps and minimal immersions. In this talk, I'll
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
The Maths of General Relativity (4/8) - Metric tensor
In this series, we build together the theory of general relativity. This fourth video focuses on the notion of metric tensor, its relations to the Christoffel symbols, and physical distances. For more videos, subscribe to the YouTube channel : https://www.youtube.com/ScienceClicEN And if
From playlist The Maths of General Relativity