Definition:Neighborhood Filter

Definition

Let $X$ be a topological space.

Let $A \subseteq X$ such that $A \ne \varnothing$.

Let $\mathcal N$ be the set of all neighborhoods of $A$.

Then $\mathcal N$ is the neighborhood filter of $A$.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$: Filters