Nearly metacompact 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 said to be nearly metacompact if given any open cover, we can find a dense subset of the topological space, and a refinement of the open cover, that is point-finite on the dense subset.

Formalisms

Template:Refinement formal expression

Open \to Open, point-finite on a dense subset

Relation with other properties

Stronger properties