Definition:Limit Point/Filter Basis/Definition 1

Definition

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 $\FF$.

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 $x$.

Also see

• Equivalence of Definitions of Limit Point of Filter Basis

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: Filters