Category:Disjoint Compact Set and Closed Set in Topological Vector Space separated by Open Neighborhood

This category contains pages concerning Disjoint Compact Set and Closed Set in Topological Vector Space separated by Open Neighborhood:

Let $F$ be a topological field.

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

Let $K$ be a compact subspace of $X$.

Let $C \subseteq X$ be a closed set such that:

$K \cap C = \O$

Then there exists an open neighborhood $V$ of ${\mathbf 0}_X$ such that:

$\paren {K + V} \cap \paren {C + V} = \O$