[[Functional analysis MOC]]
# Topological vector space

A **topological vector space** is a [[vector space]] $(V,\mathbb{K})$ over a [[topological field]] $\mathbb{K}$ equipped with a [[Topological space|topology]] 
such that scalar multiplication $(\cdot) : \mathbb{K} \times V \to V$ and vector addition $(+) : V \times V \to V$ are [[Continuity|continuous]]. #m/def/anal/fun 

## Properties

- A topological vector space is a form of [[Topological group]]

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#state/tidy | #lang/en | #SemBr