Definition:Metacompact Space

Definition

Let $T = \struct {S, \tau}$ be a topological space.

$T$ is metacompact if and only if every open cover of $S$ has an open refinement which is point finite.

Also known as

A metacompact space is also referred to as a pointwise paracompact space.

Also see

• Definition:Countably Metacompact Space

• Definition:Paracompact Space
• Definition:Countably Paracompact Space

• Results about metacompact spaces can be found here.

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Paracompactness