Definition:Star (Topology)

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Definition

Let be a set.

Let be a cover for .

Let .

The star of (with respect to ) is defined as:

That is, the union of all sets in which contain .

Sources

Lynn Arthur Steen and J. Arthur Seebach, Jr.:Counterexamples in Topology (1970)... (previous)...(next): : Paracompactness

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Category: Definitions/Covers

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S

C S

x ∈ S

x C

:= ⋃ {U ∈ C : x ∈ U}x∗

C x

I : §3

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