Definition:Locally Finite Cover
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Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $\CC$ be a cover of $S$.
Then $\CC$ is locally finite if and only if each element of $S$ has a neighborhood which intersects a finite number of sets in $\CC$.
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 $3$: Compactness: Paracompactness