Category:Definitions/Limit Points of Filter Bases

This category contains definitions related to Limit Points of Filter Bases.
Related results can be found in Category:Limit Points of Filter Bases.

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

Let $\FF$ be a filter on the underlying set $S$ of $T$.

Let $\BB$ be a filter basis of $\FF$.

Definition 1

A point $x \in S$ is called a limit point of $\BB$ if and only if $\FF$ converges on $x$.

$\BB$ is likewise said to converge on $x$.

Definition 2

A point $x \in S$ is called a limit point of $\BB$ if and only if every neighborhood of $x$ contains a set of $\BB$.