Topology where infinite sets are closed is the discrete
137075
If a topology contains all infinite subsets, then it is the discrete topology
127173
Closed subset of compact set is compact
102048
Closure of a compact set in Regular space $ X $
84512
The preimage of continuous function on a closed set is closed.
41339
Why do we require a topological space to be closed under finite intersection?
154682
G/H is Hausdorff implies H is closed (General topology, Volume 1 by N. Bourbaki)
2198
Maps from subsets of $\mathbb{R}^2$ that are either open/closed/continuous
36237
Closed set mapped to itself in a compact Hausdorff space
100476
Why does a Hausdorff but not countably compact space have an infinite closed discrete subset?
128118
Is the cofinite topology on a countable set first countable?
152976
Real Analysis: open and closed sets
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
130361
Basis for a topology with a countable number of sets
88823
How can the empty set be open in the definition of the cofinite topology?
41690
Products of Continuous functions: Topology
152465
Find the intersection of all $T_2$ topologies on an infinite set $X$
99236
Interior of closure of an open set