Assertion: open cover | /r/HasAspect | point-finite open refinement
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.
text: 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.