Metacompact space

Definition
A topological space is said to be metacompact if it satisfies the following property: every open cover has a point-finite open refinement.

Metaproperties
A direct product of metacompact spaces need not be metacompact. However, it follows from the tube lemma that a direct product of a metacompact space with a compact space is metacompact.

Textbook references

 * , Page 152 (formal definition)