Prove that a subset is closed
73353
Is it true that a subset that is closed in a closed subspace of a topological space is closed in the whole space?
109682
Proposed proof of: If $A \subset B \subset \bar{A}$ and $A$ is connected, then $B$ is connected
143457
Is product of two closed sets closed?
28683
Sum of two closed sets in $\mathbb R$ is closed?
95244
Prove that a finite union of closed sets is also closed
127173
Closed subset of compact set is compact
78300
Showing a set is closed other than giving a counterexample?
104855
Prove that $N \subset Z(G)$
130975
Given a pair of continuous functions from a topological space to an ordered set, how to prove that this set is closed?
13848
Showing that if a subset of a complete metric space is closed, it is also complete
33310
Proving that the set of limit points of a set is closed
6291
Proving something is a linearly independent subset
40162
Prove that the set $\mathbb{Q}[\alpha] = \{a+b\alpha+c\alpha^2 \mid a, b, c \in\mathbb{Q}\}$ is closed under addition and multiplication.
111538
If $S \subseteq X$ is closed, is $f(S,r)$ necessarily closed?
146146
Proof that a closed subset of a compact space is a compact space
105886
A question on the proof of 14 distinct sets can be formed by complementation and closure
5448
Finding the closure of some subsets of the ordered square