Show that $G_k$ is an open subset of $\mathbb{R}$ for each $k \in \mathbb{Z}^+$
42084
Set of points of continuity are $G_{\delta}$
135611
Extensions of $\mathbb{Z}$ by $\mathbb{Z}$
31710
Show that $\mathcal{J}=\{[a, a+1) \mid a \in \mathbb{R}\}$ generates the Borel set of $\mathbb{R}$
82824
Affine algebraic subset of $\mathbb{A}_k^4$
92740
prove that $\mathbb{Q}^n$is dense subset of $\mathbb{R^n}$
51687
Is the set $ \ (\mathbb{Z}_p \setminus \mathbb{Z}) \cap \mathbb{Q}$ non-empty?
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
117781
Proving that $S=\{\frac{1}{n}:n\in\mathbb{Z}\}\cup\{0\}$ is compact using the open cover definition
152927
seemingly nontrivial question about covering maps and evenly covered open sets
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
75829
Dimension of open subsets of $R^n$
132541
Showing ${1\over n}\sum|S_i|=O(\sqrt n)$ for $S_i\subset [n]$, $|S_i\cap S_i|\le 1$ for $i\ne j$
70264
Prove that the inverse image of an open set is open
44704
familly of Radially open sets in $\mathbb{R}^2$
93169
Show that $(\mathbb Z[x],+)$ and $(\mathbb Q_{>0},\cdot)$ are isomorphic groups
158569
Proving a particular subset of $R^n$ is closed
79424
Don't understand proof that interior of a set is open