Category:Dilation of Closure of Set in Topological Vector Space is Closure of Dilation

This category contains pages concerning Dilation of Closed Set in Topological Vector Space is Closed Set:

Let $K$ be a topological field.

Let $X$ be a topological vector space over $K$.

Let $F$ be a closed set in $X$.

Let $\lambda \in K \setminus \set {0_K}$.

Then $\lambda F$ is a closed set in $X$.