Definition:Open Neighborhood/Point

Definition

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

Let $x \in S$ be a point of $S$.

Let $N_x$ be a neighborhood of $x$ in $T$.

Let:

$N_x \in \tau$

That is, let $N_x$ itself be an open set of $T$.

Then $N_x$ is called an open neighborhood of $x$ in $T$.

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
• 1991: Walter Rudin: Functional Analysis (2nd ed.) ... (previous) ... (next): $1.5$: Topological spaces