Hausdorff space

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

Impressionen Bonner Mathematikturnier 2021

From playlist Hausdorff Center goes public

Hausdorff School: Introduction by Karl-Theodor Sturm

Presentation of the Hausdorff School by Karl-Theodor Sturm, coordinator of the Hausdorff Center. 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.

From playlist Inauguration of Hausdorff School 2015

Hausdorff School: Lecture by Jean-Pierre Bourguignon

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 Jean-Pierre Bourguignon on "Sound, Shape, and Harmony –

From playlist Inauguration of Hausdorff School 2015

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

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 Center for Mathematics

The Hausdorff Center for Mathematics (HCM) capitalizes on a broad vision of mathematics, ranging from pure mathematics, to contributions to quantative modeling in economics and the natural sciences, to industrial applications. HCM strives to serve the international mathematical community a

From playlist Hausdorff Center goes public

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

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

MAST30026 Lecture 12: Function spaces (Part 2)

The aim of this lecture was to motivate the definition of the compact-open topology on function spaces, via the adjunction property. I explained how any topology making the adjunction property true must include a certain class of open sets, which we will define next lecture to be a sub-bas

From playlist MAST30026 Metric and Hilbert spaces

MAST30026 Lecture 12: Function spaces (Part 3)

We continued the discussion of the compact-open topology on function spaces. Guided by Part 2 we defined this topology, and got about half way through the proof that the adjunction property (aka the exponential law) holds when function spaces are given this topology. Lecture notes: http:/

From playlist MAST30026 Metric and Hilbert spaces

MAST30026 Lecture 11: Hausdorff spaces (Part 2)

This lecture contains the first half of the proof that a finite CW-complex is a Hausdorff space. Lecture notes: http://therisingsea.org/notes/mast30026/lecture11.pdf The class webpage: http://therisingsea.org/post/mast30026/ Have questions? I hold free public online office hours for this

From playlist MAST30026 Metric and Hilbert spaces

Henry Adams (3/22/22): Gromov-Hausdorff distances, Borsuk-Ulam theorems, and Vietoris-Rips complexes

The Gromov-Hausdorff distance between two metric spaces is an important tool in geometry, but it is difficult to compute. For example, the Gromov-Hausdorff distance between unit spheres of different dimensions is unknown in nearly all cases. I will introduce recent work by Lim, Mémoli, and

From playlist Vietoris-Rips Seminar

What is a Manifold? Lesson 15: The cylinder as a quotient space

What is a Manifold? Lesson 15: The cylinder as a quotient space This lesson covers several different ideas on the way to showing how the cylinder can be described as a quotient space. Lot's of ideas in this lecture! ... too many probably....

From playlist What is a Manifold?

MAST30026 Lecture 11: Hausdorff spaces (Part 3)

This lecture contains the second half of the proof that a finite CW-complex is a Hausdorff space. Lecture notes: http://therisingsea.org/notes/mast30026/lecture11.pdf The class webpage: http://therisingsea.org/post/mast30026/ Have questions? I hold free public online office hours for thi

From playlist MAST30026 Metric and Hilbert spaces

Hausdorff School für Mathematik-Nachwuchs eröffnet

Die Hausdorff School ist ein neuartiges, strukturiertes Ausbildungsprogramm für promovierte Nachwuchswissenschaftler, errichtet vom Hausdorff Center for Mathematics der Universität Bonn. Vor dem Festakt sprach uni-bonn.tv mit dem Rektor der Universität, Prof. Dr. Michael Hoch. Team: Marcu

From playlist Inauguration of Hausdorff School 2015

MAST30026 Lecture 12: Function spaces (Part 4)

We completed the proof that the adjunction property holds for the space of continuous functions from a locally compact Hausdorff space, reminded ourselves of some of the immediate consequences of this theorem, and then began motivating the construction of a metric on function spaces. Lect

From playlist MAST30026 Metric and Hilbert spaces