Feebly compact space

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This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
This is a variation of compactness. View other variations of compactness

Definition

A topological space is termed feebly compact or lightly compact if every locally finite collection of nonempty open subsets is finite.

Relation with other properties

Stronger properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Compact space Every open cover has a finite subcover compact implies feebly compact feebly compact not implies compact |FULL LIST, MORE INFO

Weaker properties

property quick description proof of implication proof of strictness (reverse implication failure) intermediate notions
Pseudocompact space Image of continuous map to reals is bounded feebly compact implies pseudocompact pseudocompact not implies feebly compact |FULL LIST, MORE INFO