Definition:Limit Point/Filter
< Definition:Limit Point(Redirected from Definition:Limit Point of Filter)
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $\FF$ be a filter on $S$.
A point $x \in S$ is called a limit point of $\FF$ if and only if $\FF$ is finer than the neighborhood filter of $x$.
Also see
- Results about filters can be found here.
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