$A, B \subset X$ compact, disjoint subsets of a Hausdorff space. Show existence of disjoint empty sets
11383
Disjoint compact sets in a Hausdorff space can be separated
55374
Cover of (0,1) with no finite subcover & Open sets of compact function spaces
28391
Prove the compactness of a set B
157218
If $E\subseteq X$ is connected, $E\cap A\neq\emptyset$ and $E\cap(X\setminus A)\neq\emptyset$ then $E\cap\partial A\neq\emptyset$
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)
147213
Prove that finite unions of compact sets are compact
70785
A finite Hausdorff space is discrete
61930
Intersection of Closed and Compact Set is Closed
147331
Compactness and Hausdorffness
71653
Why is the Cartesian product of a set $A$ and empty set an empty set?
6523
Prove that the space has a countable dense subset
858
Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?
39076
Contraction of compact sets
11114
Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
65976
in a topological space only finite subsets are compact sets
131983
Prove that $A \subset B$ if and only if $A \setminus B = \emptyset$
128730
Open subspaces of locally compact Hausdorff spaces are locally compact