Metacompact space

In mathematics, in the field of general topology, a topological space is said to be metacompact if every open cover has a point finite open refinement. That is, given any open cover of the topological space, there is a refinement which is again an open cover with the property that every point is contained only in finitely many sets of the refining cover.
A space is countably metacompact if every countable open cover has a point finite open refinement.
Properties.
The following can be said about metacompactness in relation to other properties of topological spaces:
Covering dimension.
A topological space "X" is said to be of covering dimension "n" if every open cover of "X" has a point finite open refinement such that no point of "X" is included in more than "n" + 1 sets in the refinement and if "n" is the minimum value for which this is true. If no such minimal "n" exists, the space is said to be of infinite covering dimension.