# Topological Vector Space

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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