In mathematics, in the field of topology, a topological space is said to be a-paracompact if every open cover of the space has a locally finite refinement. In contrast to the definition of paracompactness, the refinement is not required to be open. Every paracompact space is a-paracompact, and in regular spaces the two notions coincide. (Wikipedia).

Interstellar flight: 10 Hard Facts

We can build powerful rockets able to carry people and machines into orbit, or even vault them to the moon. But our fastest spacecraft don't hold a candle to the distances that define Interstellar Flight. So what's on the drawing boards? What futuristic designs and fuel options promise to

From playlist Spaceten

Geometry of Surfaces - Topological Surfaces Lecture 1 : Oxford Mathematics 3rd Year Student Lecture

This is the first of four lectures from Dominic Joyce's 3rd Year Geometry of Surfaces course. The four lectures cover topological surfaces and conclude with a big result, namely the classification of surfaces. This lecture provides an introduction to the course and to topological surfaces.

From playlist Oxford Mathematics Student Lectures - Geometry of Surfaces

Charles Rezk - 4/4 Higher Topos Theory

Course at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/RezkNotesToposesOnlinePart4.pdf In this series of lectures I will give an introduction to the concept of "infinity

From playlist Toposes online

Manifolds 1.4 : Topological Properties

In this video, I introduce the fact that manifolds have a countable basis of precompact coordinate balls, are locally compact, are locally path connected, and are paracompact. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Playlist : https://w

From playlist Manifolds

The International Space Station continues an uninterrupted human presence in space as a test-bed for future exploration beyond low-Earth orbit and the only science lab in microgravity. This music video featuring the space station and its crews is set to the song "World" by recording artist

From playlist Real Space Stations - YouTube Space Lab with Liam & Brad

A01 An introduction to a series on space medicine

A new series on space medicine.

From playlist Space Medicine

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

Bradley Nelson (2/19/22): Parameterized Vietoris-Rips Filtrations via Covers

A challenge in computational topology is to deal with large filtered geometric complexes built from point cloud data such as Vietoris-Rips filtrations. This has led to the development of schemes for parallel computation and compression which restrict simplices to lie in open sets in a cove

From playlist Vietoris-Rips Seminar

What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:

From playlist Science Unplugged: Physics

The Militarization of Space. Do We Really Need a Space Force?

President Trump recently called for the creation of a space force to deal with the future warfighting in space. It turns out, this already exists, space is already well militarized. Audio Podcast version: ITunes: https://itunes.apple.com/us/podcast/universe-today-guide-to-space-audio/id79

From playlist Guide to Space

B03 Fluid shifts here on earth

The difference between the erect and supine positions here on earth.

From playlist Space Medicine

"Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu"

From playlist Science Unplugged: Special Relativity

This video explains the definition of a vector space and provides examples of vector spaces.

From playlist Vector Spaces

CGSR Seminar Series | War in Space: Strategy, Spacepower, Geopolitics

Speaker Biography Bleddyn Bowen primary research interests concern modern warfare, politics, and security in outer space, as well as classical strategic theory. Dr. Bowen provides research-led teaching in his 3rd year specialist module PL3144 Politics and War in Outer Space. He is the au

From playlist Center for Global Security Research

10. The Four Fundamental Subspaces

MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 10. The Four Fundamental Subspaces License: Creative Commons BY-NC-SA More information at http

From playlist MIT 18.06 Linear Algebra, Spring 2005

[Lesson 11] QED Prerequisites - Tensor Product Spaces

We take a detour from the Angular Momentum Mind Map to cover the important topic of Tensor Product spaces in the Dirac Formalism. In quantum mechanics, the notion of tensors is hidden under the hood of the formalism and this lesson opens that hood. The goal is to make us confident that we

From playlist QED- Prerequisite Topics

Nicolò Zava (3/17/23): Every stable invariant of finite metric spaces produces false positives

In computational topology and geometry, the Gromov-Hausdorff distance between metric spaces provides a theoretical framework to tackle the problem of shape recognition and comparison. However, the direct computation of the Gromov-Hausdorff distance between finite metric spaces is known to

From playlist Vietoris-Rips Seminar

Covariant Phase Space with Boundaries - Daniel Harlow

More videos on http://video.ias.edu

From playlist Natural Sciences

CGSR Seminar Series | U.S. National Security Space Strategy: The Cold War to the Present

Talk Abstract At the present time, U.S. government officials are faced with the increasingly complex task of protecting critical national security space infrastructure in a rapidly evolving threat environment. When placed in a historical context, we find that anxiety about space security

From playlist Center for Global Security Research