Linear topological space | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-05-03

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Topological_vector_space


00:01:15 1 Definition
00:02:44 2 Examples
00:04:34 2.1 Product vector spaces
00:05:51 3 Topological structure
00:10:00 4 Local notions
00:11:51 5 Types
00:16:45 6 Dual space



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SUMMARY
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In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis. A topological vector space is a vector space (an algebraic structure) which is also a topological space, thereby admitting a notion of continuity.  More specifically,  its topological space has a uniform topological structure, allowing a notion of uniform convergence.
The elements of topological vector spaces are typically 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.
Hilbert spaces and Banach spaces are well-known examples.
Unless stated otherwise, the underlying field of a topological vector space is assumed to be either the complex numbers C or the real numbers R.