Articles containing proofs | Topology of function spaces | Vector spaces | Topological spaces | Topological vector spaces
In mathematics, a topological vector space (also called a linear topological space and commonly abbreviated TVS or t.v.s.) is one of the basic structures investigated in functional analysis.A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar multiplication) are also continuous functions. Such a topology is called a vector topology and every topological vector space has a uniform topological structure, allowing a notion of uniform convergence and completeness. Some authors also require that the space is a Hausdorff space (although this article does not). One of the most widely studied categories of TVSs are locally convex topological vector spaces. This article focuses on TVSs that are not necessarily locally convex. Banach spaces, Hilbert spaces and Sobolev spaces are other well-known examples of TVSs. Many topological vector spaces are spaces of functions, or linear operators acting on topological vector spaces, and the topology is often defined so as to capture a particular notion of convergence of sequences of functions. In this article, the scalar field of a topological vector space will be assumed to be either the complex numbers or the real numbers unless clearly stated otherwise. (Wikipedia).
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
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From playlist Linear Algebra
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 video is about topological spaces and some of their basic properties.
From playlist Basics: Topology
When learning linear algebra, we will frequently hear the term "vector space". What is that? What are the requirements for being considered a vector space? Let's go over the properties of closure that are associated with vector spaces so that we can understand this important concept. Scri
From playlist Mathematics (All Of It)
linear algebra vector space (25 examples)
Vector Spaces. Definition and 25 examples. Featuring Span and Nul. Hopefully after this video vector spaces won't seem so mysterious any more! Check out my Vector Space playlist: https://www.youtube.com/watch?v=mU7DHh6KNzI&list=PLJb1qAQIrmmClZt_Jr192Dc_5I2J3vtYB Subscribe to my channel:
From playlist Vector Spaces
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
Foundations of Quantum Mechanics: Topology of a vector space
Foundations of Quantum Mechanics: Topology of a vector space This lecture explores how a norm induces a rather obvious topology on a vector space. We also dive deep into some analysis to prove a few interesting lemmas about normed vector spaces. We demonstrate the interesting result that
From playlist Mathematical Foundations of Quantum Mechanics
This video is about metric spaces and some of their basic properties.
From playlist Basics: Topology
Foundations of QM: Introduction Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX and discussing the material on the forums: https://www.patreon.com/XYLYXYLYX
From playlist Mathematical Foundations of Quantum Mechanics
Even spaces and motivic resolutions - Michael Hopkins
Vladimir Voevodsky Memorial Conference Topic: Even spaces and motivic resolutions Speaker: Michael Hopkins Affiliation: Harvard University Date: September 13, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
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I began by proving the universal property of the completion of a normed space. I then discussed characterisations of finite-dimensionality for vector spaces, introduced the continuous linear dual for normed spaces and the operator norm, and stated the duality theorem or L^p spaces which sa
From playlist MAST30026 Metric and Hilbert spaces
Konrad Polthier (7/27/22): Boundary-sensitive Hodge decompositions
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From playlist Applied Geometry for Data Sciences 2022
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Talk by Dustin Clausen in Global Noncommutative Geometry Seminar (Americas) on November 12, 2021.
From playlist Global Noncommutative Geometry Seminar (Americas)
Giuseppe De Nittis : Topological nature of the Fu-Kane-Mele invariants
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From playlist Mathematical Physics
Index Theory, survey - Stephan Stolz [2018]
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From playlist Mathematics
After our introduction to matrices and vectors and our first deeper dive into matrices, it is time for us to start the deeper dive into vectors. Vector spaces can be vectors, matrices, and even function. In this video I talk about vector spaces, subspaces, and the porperties of vector sp
From playlist Introducing linear algebra
algebraic geometry 5 Affine space and the Zariski topology
This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of affine space and its Zariski topology.
From playlist Algebraic geometry I: Varieties