What does "metacompact" mean?

Of a topological space: such that 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.

Metacompact

adj

adj ·Rare ·Advanced level

Definitions

Adjective

1
Of a topological space: such that 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. not-comparable

Etymology

From meta- + compact.

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.