Definition:Open Neighborhood/Topology

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Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $A \subseteq S$ be a subset of $S$.

Let $N_A$ be a neighborhood of $A$.


If $N_A \in \tau$, i.e. if $N_A$ is itself open in $T$, then $N_A$ is called an open neighborhood.


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