Assertion: cover's refinement | /r/HasProperty | countable
Facets:
Source sentences:
text: Compact if every open cover has a finite subcover, (or equivalently that every open cover has a finite refinement); Lindelöf if every open cover has a countable subcover, (or equivalently that every open cover has a countable refinement); Metacompact if every open cover has a point-finite open refinement; Paracompact if every open cover admits a locally finite open refinement.