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locally closed∗
asteroid†
2013-03-21 23:56:53
Definition - A subset Y of a topological space X is said to be locally
closed if it is the intersection of an open and a closed subset.
The following result provides some equivalent definitions:
Proposition - The following are equivalent:
1. Y is locally closed in X.
2. Each point in Y has an open neighborhood U ⊆ X such that U ∩ Y is
closed in U (with the subspace topology).
3. Y is open in its closure Y (with the subspace topology).
∗ hLocallyClosedi created: h2013-03-21i by: hasteroidi version: h40018i Privacy setting:
h1i hDefinitioni h54D99i
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