Give examples of compact spaces $A,B$ such that $A\cap B$ is not compact
55648
Intersection of finite number of compact sets is compact?
72875
"Naturally occurring" non-Hausdorff spaces?
148403
Compact space and Hausdorff space
22854
Let $A , B\subseteq\mathbb{R}$. If $A$ is closed and $B$ is compact, is $A\cdot B$ closed?
10034
Give an example of a non-separable subspace of a separable space
59275
If $X$ is an infinite set, then $X$ with the discrete topology is not compact
116112
Examples of 'almost' vector spaces where unitary law fails
127166
Specific example of a space that is separable but not second countable.
136108
Arbitrary intersection of closed, connected subsets of a compact space connected?
116542
Which of the following sets are compact in $\mathbb{M}_n(\mathbb{R})$[NBHM_PhD Screening Test-2013, Topology]
98391
example of a nonempty subset is closed under scalar multiplication but not a subspace
73154
Compact subset in colimit of spaces
64840
A Banach space that is not a Hilbert space
18040
Show that a compact metric space is bounded
102048
Closure of a compact set in Regular space $ X $
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly