Definition:Neighborhood Filter/Set

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $A \subseteq S$ such that $A \ne \O$.

Let $\NN_A$ be the set of all neighborhoods of $A$.

Then $\NN_A$ is the neighborhood filter of $A$.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Filters