# Nearly metacompact space

From Topospaces

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 Open, point-finite on a dense subset