Every closed set in a separable metric space is the union of a perfect set and a set which is at most countable
17842
Is every set in a separable metric space the union of a perfect set and a set that is at most countable?
111360
Topological spaces in which every proper closed subset is compact
114608
Proof concerning regular space: there exist a closed set contained in any open set containing $x$
33157
Proof that an infinite subset of $\mathbb{N}$ is countable
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
125962
The set $A'$ is closed in a $T_1$ space
33859
How to show that a disjoint sum of metric spaces is metrizable?
63276
Is an arbitrary union of a chain of countable sets countable?
17733
$X$ second countable locally compact Hausdorff implies $C(X)$ separable?
95244
Prove that a finite union of closed sets is also closed
68230
The cardinality of a countable union of sets with less than continuum cardinality
41192
Neatest proof that set of finite subsets is countable?
102048
Closure of a compact set in Regular space $ X $
143484
A separable locally compact metric space is compact iff all of its homeomorphic metric spaces are bounded
16060
Showing this metric space is complete
127173
Closed subset of compact set is compact