Definition:Limit Point/Filter Basis/Definition 2
Jump to navigation
Jump to search
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 every neighborhood of $x$ contains a set of $\BB$.
Also see
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