# Definition:Neighborhood Filter/Point

< Definition:Neighborhood Filter(Redirected from Definition:Neighborhood Filter of Point)

Jump to navigation
Jump to search
## 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 $3.2$