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locally finite (Definition)

A collection $ \mathcal{U}$ of subsets of a topological space $ X$ is said to be locally finite if whenever $ x\in X$ there is an open set $ V \subseteq X$ with $ x \in V$ such that $ V \cap U = \varnothing$ for all but finitely many $ U \in \mathcal{U}$.



"locally finite" is owned by yark. [ full author list (2) | owner history (1) ]
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See Also: point finite

Also defines:  locally finite collection
Keywords:  topology

Attachments:
the union of a locally finite collection of closed sets is closed (Theorem) by yark
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Cross-references: open set, topological space, subsets, collection
There are 9 references to this entry.

This is version 5 of locally finite, born on 2002-01-22, modified 2006-11-08.
Object id is 1542, canonical name is LocallyFinite.
Accessed 3599 times total.

Classification:
AMS MSC: 54D20 (General topology :: Fairly general properties :: Noncompact covering properties )
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