Separating disjoint compact sets in Hausdorff space by using open sets
11383
Disjoint compact sets in a Hausdorff space can be separated
81351
Polish space in which the interior of each compact set is empty
16654
Unions and Intersections of Open Sets are Open
42698
Set of limit points of a subset of a Hausdorff space is closed.
113534
Show that any metrizable space $X$ is Hausdorff
149426
Is there a Hausdorff space $X$ separating points of any Hausdorff space?
104769
Any two points in a Stone space can be disconnected by clopen sets
136094
$G_\delta$ singletons in compact Hausdorff and first countability
27998
Prove existence of disjoint open sets containing disjoint closed sets in a topology induced by a metric.
73154
Compact subset in colimit of spaces
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
29303
Cartesian product of compact sets is compact
71916
Quasi-components and components coincide for compact Hausdorff spaces
115625
Intersection of two open dense sets is dense
41611
Open and closed set in n by n matrices space.
27517
Isometry in compact metric spaces
79779
How big can a separable Hausdorff space be?