General topology | Properties of topological spaces
In mathematics, a topological space is called separable if it contains a countable, dense subset; that is, there exists a sequence of elements of the space such that every nonempty open subset of the space contains at least one element of the sequence. Like the other axioms of countability, separability is a "limitation on size", not necessarily in terms of cardinality (though, in the presence of the Hausdorff axiom, this does turn out to be the case; see below) but in a more subtle topological sense. In particular, every continuous function on a separable space whose image is a subset of a Hausdorff space is determined by its values on the countable dense subset. Contrast separability with the related notion of second countability, which is in general stronger but equivalent on the class of metrizable spaces. (Wikipedia).
Andrej Bauer: Every metric space is separable in function realizability
The lecture was held within the framework of the Hausdorff Trimester Program: Constructive Mathematics. Abstract: I first show that in the function realizability topos every metric space is separable, and every object with decidable equality is countable. More generally, working with syn
From playlist Workshop: "Constructive Mathematics"
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
If the universe is spatially infinite, what can we say about reality...
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From playlist Science Unplugged: Cosmology
This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.
From playlist Proofs
Is there any place in the Universe where there's truly nothing? Consider the gaps between stars and galaxies? Or the gaps between atoms? What are the properties of nothing?
From playlist Guide to Space
This video is about separability properties of spaces.
From playlist Basics: Topology
Covariant Phase Space with Boundaries - Daniel Harlow
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From playlist Natural Sciences
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From playlist Science Unplugged: Special Relativity
SEPARATION BUT MATHEMATICALLY: What Types of Mathematical Topologies are there? | Nathan Dalaklis
The title of this video is a bit convoluted. What do you mean by "Separation but Mathematically"? Well, in this video I'll be giving a (very diluted) answer to the question "What types of mathematical topologies are there?" by introducing the separation axioms in topology. The separation
From playlist The New CHALKboard
(January 28, 2013) Leonard Susskind presents three possible geometries of homogeneous space: flat, spherical, and hyperbolic, and develops the metric for these spatial geometries in spherical coordinates. Originally presented in the Stanford Continuing Studies Program. Stanford Universit
From playlist Lecture Collection | Cosmology
Wolfram Physics IV: Multiway Invariance and Advanced Quantum Mechanics
Find more information about the summer school here: https://education.wolfram.com/summer/school Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/physics-announcement Find the tools to build a universe: https:
From playlist Wolfram Summer Programs
Wolfram Physics Project: Working Session Saturday, June 27, 2020 [Multiway Systems]
This is a Wolfram Physics Project working session on multiway systems in the Wolfram Model. Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcement post: http://wolfr.am/phys
From playlist Wolfram Physics Project Livestream Archive
Support Vector Machines - Part 4: Nonlinear SVMs
This video is about Support Vector Machines - Part 4: Nonlinear SVMs Abstract: This is a series of videos about Support Vector Machines (SVMs), which will walk through the introduction, the working principle and theory covering a linearly separable case, non-separable case, nonlinear SVM
From playlist Machine Learning
Data Science - Part IX - Support Vector Machine
For downloadable versions of these lectures, please go to the following link: http://www.slideshare.net/DerekKane/presentations https://github.com/DerekKane/YouTube-Tutorials This lecture provides an overview of Support Vector Machines in a more relatable and accessible manner. We will g
From playlist Data Science
38th Annual Geometric Topology Workshop (Online), June 15-17, 2021 Eric Swenson, Brigham Young University Title: Cuts and blobs Abstract: We provide sharp conditions under which a collection of separators of a connected topological space leads to a canonical -tree . Any group acting on
From playlist 38th Annual Geometric Topology Workshop (Online), June 15-17, 2021
Some 20+ year old problems about Banach spaces and operators on them – W. Johnson – ICM2018
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From playlist Analysis & Operator Algebras
Mateusz Skomora: Separation theorems in signed tropical convexities
The max-plus semifield can be equipped with a natural notion of convexity called the “tropical convexity”. This convexity has many similarities with the standard convexity over the nonnegative real numbers. In particular, it has been shown that tropical polyhedra are closely related to the
From playlist Workshop: Tropical geometry and the geometry of linear programming
Beyond the Basic Stuff with Python - Al Sweigart - Part 10
This is video 10 of my 54-video online course following my free book, "Beyond the Basic Stuff with Python". This book is written for intermediate programmers, and can be read online at https://inventwithpython.com/beyond/ Support me on Patreon: https://patreon.com/AlSweigart Skip Amazon
From playlist Beyond the Basic Stuff with Python
Uri Bader - 1/4 Algebraic Representations of Ergodic Actions
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From playlist Uri Bader - Algebraic Representations of Ergodic Actions
A short video on terms such as Vector Space, SubSpace, Span, Basis, Dimension, Rank, NullSpace, Col space, Row Space, Range, Kernel,..
From playlist Tutorial 4