Prove that $\mathbb{Z}$ is a closed subset of $\mathbb{R}$
103717
Topological Property of the Set of Integers
42145
Prove that the only sets in $R$ which are both open and closed are the empty set and $R$ itself.
46917
How to prove that $GL(n,\mathbb R)$ is not connected subset and open subset of$M_n (\mathbb{R})$
44704
familly of Radially open sets in $\mathbb{R}^2$
66239
Verifying that a certain collection of intervals of $\mathbb R$ forms a topology
10180
How to prove that this set is closed?
47680
Prove that the union of the interior of a set and the boundary of the set is the closure of the set
101669
Cardinality of the Set of all finite subset of $\mathbb{R}$
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
74330
$\mathbb{R}^n$ not homeomorphic to open subset of $\mathbb{R}^m$
140570
Suppose $E\subseteq\mathbb{R}$ is closed and $K\subseteq\mathbb{R}$ is compact. Show that every open cover of $E\cap K$ has a finite subcover
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
22464
Which of the following subsets of   $\mathbb{R}^2$ are compact
30411
The closure of the irrational numbers on $\mathbb{R}$
127575
Prove that Open Sets in $\mathbb{R}$ are The Disjoint Union of Open Intervals Without the Axioms of Choice
21114
$S=\{(n,{1\over n}):n\in\mathbb{N}\}$ is closed in $X$?
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set