Compactness & countable dense subset
7402
Showing a compact metric space has a countable dense subset
9268
Proving that the Union of Two Compact Sets is Compact
73154
Compact subset in colimit of spaces
17733
$X$ second countable locally compact Hausdorff implies $C(X)$ separable?
44974
Infinite set and countable subsets
67259
Can we prove that a bounded closed subset of $\mathbb R^n$ is compact without Axiom of Choice?
57839
Real analysis: density and continuity
148994
$K \subset \mathbb{R}^n$ is compact iff it is closed and bounded
23442
Cardinality of the union of infinite and countable sets
98609
Does pointwise equicontinuous and uniformly equicontinuous implies compactness?
147136
Subset of a countable set is itself countable
9021
An infinite subset of a countable set is countable
11114
Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
45249
Pseudocompactness does not imply compactness
144400
Are compact subsets of metric spaces closed and bounded?
29303
Cartesian product of compact sets is compact
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$