If a topological space is covered by finitely many closed sets, then one of them has nonempty interior
94825
Open set as a finite union of closed sets
72190
Topological proof on discrete topology where $X$ is infinite
42494
The boundary is a closed set
73336
If $A$ is a nowhere dense subset of a topological space $X$, then $X\setminus A$ is dense in $X$.
15480
Open set in a metric space is union of closed sets
158498
$A\subset \mathbb{R}$ with more than one element and $A/ \{a\}$ is compact for a fixed $a\in A$
78513
Show finite complement topology is, in fact, a topology
103769
The Cartesian product of a finite number of countable sets is countable
18039
Let $A$ be a dense subset of $X$ and suppose $A$ is connected in the induced subspace topology, then $X$ is also connected
11405
If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
2866
Given a countable partition of the reals, must the condensation points of some part have nonempty interior?
78399
In $T_1$ space, all singleton sets are closed?
70048
In which topologies do open sets maintain open under countable or arbitrary intersection?
148213
Given a topological space $X$, why are both $X$ and $\emptyset$ open and closed?
154559
For each $x\in X$ there exists a neighborhood of x s.t $A\cap U\neq \emptyset$ for only finitely many $A\in\mathcal{A}$. Show that f is continuous.
3896
A closed set in $(A, \mathcal T_A)$ that is not closed in $(X, \mathcal T)$
82825
Proving set of interiors is open