Category:Open Neighborhood of Point in Topological Vector Space contains Sum of Open Neighborhoods

This category contains pages concerning Open Neighborhood of Point in Topological Vector Space contains Sum of Open Neighborhoods:

Let $K$ be a topological field.

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

Let $a, b \in X$.

Let $W$ be an open neighborhood of $a + b$.

Then there exists an open neighborhood $W_1$ of $a$ and an open neighborhood $W_2$ of $b$ such that:

$W_1 + W_2 \subseteq W$

where $W_1 + W_2$ denotes the sum of $W_1$ and $W_2$.