Compact Hausdorf space $\implies$ not the countable union of nowhere dense sets?
120135
Show every nonempty compact Hausdorff space is not the countable union of nowhere dense sets
39842
Limit point Compactness does not imply compactness counter-example
132382
Showing a set is nowhere dense in $C([0,1])$
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
14048
Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
97064
Dense set in an infinite cofinite space
66180
Homomorphism between compact Hausdorff spaces.
92005
Existence of compact/complete metric on countable set
45249
Pseudocompactness does not imply compactness
99478
countably infinite union of countably infinite sets is countable
7402
Showing a compact metric space has a countable dense subset
55374
Cover of (0,1) with no finite subcover & Open sets of compact function spaces
62793
$\mathbb{R}$ with the lower limit topology is not second-countable
128730
Open subspaces of locally compact Hausdorff spaces are locally compact
13620
$\omega_2$ is a not countable union of countable sets without AC
44430
Is there an open dense set $S \subset [0,1]$ such that $m(S)<1$?