Is there a T0 space with a subset A such that (A')' is not a subset of A'?
74792
$(X,\tau)$ needs to be $T_1$ in order to guarantee that $A'$ is closed?
3072
If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
32819
Looking for examples of first countable, compact spaces which is not separable
78399
In $T_1$ space, all singleton sets are closed?
95635
$\ell^{\infty}(\mathbb N)$ is not a separable space
146891
Why is $\{\emptyset\} \not = \emptyset$?
80735
Show that $C_0([a, b], \mathbb{R})$ is not $\sigma$-compact
70413
A vector space over $R$ is not a countable union of proper subspaces
52014
Showing $(C[0,1], d_1)$ is not a complete metric space
72875
"Naturally occurring" non-Hausdorff spaces?
129227
An example of neither open nor closed set
154230
In $\mathsf{ZF}$, for each set $A$ exists an ordinal $\alpha$ such that no surjection $A\to \alpha$ exists
71173
Show that $\mathbb{A}^n$ on the Zariski Topology is not Hausdorff, but it is $T_1$
148025
Is there an operator for 'contained in set or subset or subset of subset' and so on?
98391
example of a nonempty subset is closed under scalar multiplication but not a subspace
7733
If A is infinite, does there have to exist a subset of A that is equivalent to A?
20706
Non-existence of a Surjective Function from a Set to Its Subsets (Cantor's theorem)