Topological Vector Space
(Redirected from Topological vector space)
A Topological Vector Space is a vector space that ...
- AKA: Linear Topological Space.
- See: Vector Space, Function (Mathematics), Linear Map, Hilbert Space, Banach Space, Complex Number.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/topological_vector_space Retrieved:2015-2-7.
- In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis. As the name suggests the space blends a topological structure (a uniform structure to be precise) with the algebraic concept of a vector space.
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.
- In mathematics, a topological vector space (also called a linear topological space) is one of the basic structures investigated in functional analysis. As the name suggests the space blends a topological structure (a uniform structure to be precise) with the algebraic concept of a vector space.