Showing that $\{(x, y) \in \mathbb{R}^2 \mid x< 0, y<0 \}$ is open
59424
Showing that $B=\{(x,y) \in \Bbb{R^2} \mid \ xy>0 \}$ is an open set
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
138931
Show that $||x+y||\cdot||x-y||\le||x||^2+||y||^2$
55484
Proving that the map from a topological space to a fiber bundle is open.
110957
No non-trivial clopen sets in $\mathbb{R}$? How to give a direct proof?
158569
Proving a particular subset of $R^n$ is closed
135454
An open interval is an open set?
778
For $x∈\mathbb{R}^n$ , let $B(x,r)$ denote the closed ball in $\mathbb{R}^n$(with Euclidean norm) of radius $r$ centered at $x$
69283
The limit points of an open interval (open set)
63442
Show that if $U$ is an open connected subspace of $\mathbb{R}^2$, then $U$ is path connected
152976
Real Analysis: open and closed sets
97761
Show that a proper continuous map from $X$ to locally compact $Y$ is closed
149317
An open subset of $\mathbb{R}$ is an at-most-countable union of disjoint open intervals
50344
What is the closure of an open ball $B_X(\mathbf{a},r)$ in $X=\mathbb{R}^n$?
149820
How do you prove the set $G = \{(x, f(x)) \mid x \in \mathbb R\}$ is closed?
110217
$GL(n,K)$ is open in $M(n,K)$
13162
Prove $\alpha \in R[[x]]$ is a unit iff $a_0 \in R$ is a unit