Definition:Neighborhood Filter/Point
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $x \in S$.
Let $\NN_x$ be the set of all neighborhoods of $x$ in $T$.
Then $\NN_x$ is the neighborhood filter of $x$ (in $T$).
Also known as
The neighborhood filter of a point can also be referred to as the system of neighborhoods or complete system of neighborhoods at that point.
Also see
Sources
- 1975: Bert Mendelson: Introduction to Topology (3rd ed.) ... (previous) ... (next): Chapter $3$: Topological Spaces: $\S 3$: Neighborhoods and Neighborhood Spaces: Definition $3.2$