The real numbers were shown to lack this property by the diagonal argument, also proposed by Cantor.
If every open cover of a topological space has a subcover with this property, it is known as a Lindelöf space. Separable spaces are those with dense subsets having this property. Powersets of sets with this property lack it according to (*) Cantor's theorem, while the set of discontinuities of monotone functions must have this property. The real numbers were shown to lack this property by the diagonal argument, also proposed by Cantor. Possessed by the integers and rationals, for 10 points, name this property of sets that can be put into bijection with the natural numbers and have cardinality denoted aleph-null.
If every open cover of a topological space has a subcover with this property, it is known as a Lindelöf space.
{countability} [accept word forms; accept {countably infinite}; prompt on {infinite} before “lack it”; accept {denumerability} or word forms thereof; accept answers involving {aleph}-{null} or {aleph}-{naught} before the end]