Definition:Neighborhood Filter/Set
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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