Disjoint compact subsets of a Hausdorff space are separated by disjoint open neighborhoods
11383
Disjoint compact sets in a Hausdorff space can be separated
6523
Prove that the space has a countable dense subset
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
41611
Open and closed set in n by n matrices space.
49039
Sets with Hausdorff-Measure 0
18572
Union of a family of connected pairwise not disjoint subspaces is connected
30231
The boundary of union is the union of boundaries when the sets have disjoint closures
84104
Definition of neighborhood and open set in topology
144383
The closure of a connected set in a topological space is connected
2978
A and B disjoint, A compact, and B closed implies there is positive distance between both sets
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
93389
Uncountable sets of Hausdorff dimension zero
15480
Open set in a metric space is union of closed sets
65976
in a topological space only finite subsets are compact sets
19566
Continuous images of compact sets are compact
127678
A partition of the unit interval into uncountably many dense uncountable subsets
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.