Characterising the discrete topology with compact subsets
65976
in a topological space only finite subsets are compact sets
1756
1-point compactification and embedding
21938
describing all possible topologies on a set
146146
Proof that a closed subset of a compact space is a compact space
73154
Compact subset in colimit of spaces
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
140168
What are the basis for co-countable and co-finite topologies
120685
Topology induced from Kuratowski Closure properties
111360
Topological spaces in which every proper closed subset is compact
111001
Does weak topology preserve topological vector space structure?
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
48369
discrete subgroups of euclidean space
88205
How can I define a topology on the empty set?
127678
A partition of the unit interval into uncountably many dense uncountable subsets
9580
Real life applications of Topology
147197
Number of connected components of the complement of a compact
72190
Topological proof on discrete topology where $X$ is infinite