Distinct Hausdorff topologies with same compact sets
481
Can compact sets completey determine a topology?
128934
Every infinite Hausdorff space has an infinite discrete subspace
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
141642
Closure of a certain subset in a compact topological group
108864
Showing that two topologies give rise to the same topology
148403
Compact space and Hausdorff space
79236
Topology on $\mathbb{R}$ strictly coarser (resp. finer) than the usual one which is still Hausdorff (resp. connected)
80180
Discrete and compact subset must be finite
100476
Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
100121
Assume that $(\text{X}, T)$ is compact and Hausdorff. Prove that a comparable but different topological space $(\text{X},T')$ is not.
37654
Topology: Example of a compact set but its closure not compact
28637
Proving continuous image of compact sets are compact
21938
describing all possible topologies on a set
41408
Which of the following sets are compact:
127173
Closed subset of compact set is compact
114123
Do the topologies with the same convergent sequences coincide?
7402
Showing a compact metric space has a countable dense subset