| A topological \PMlinkescapetext{vector space} is a pair $(V,\mathcal{T})$ where $V$ is a vector space over a topological field $K$, and $\mathcal{T}$ is a topology on $V$ such that under $\mathcal{T}$, the vector space operations $v\mapsto\lambda v$ and $(v,w)\mapsto v+w$ are continuous for all $\lambda\in K$ and all $v,w\in V$. |
A topological \PMlinkescapetext{vector space} is a pair $(V,\mathcal{T})$ where $V$ is a vector space over a field $K$, and $\mathcal{T}$ is a topology on $V$ such that under $\mathcal{T}$, the vector space operations $v\mapsto\lambda v$ and $(v,w)\mapsto v+w$ are continuous for all $\lambda\in K$ and all $v,w\in V$. |
