$(M,d)$ be a complete metric space and $N \subset M$ a closed subset $\Rightarrow N$ is complete
13848
Showing that if a subset of a complete metric space is closed, it is also complete
123061
$X$ metric separable then $C(X)$ separable
125962
The set $A'$ is closed in a $T_1$ space
80276
Metric Space & Cauchy Sequence
43376
If $A$ is compact and $B$ is closed, show $d(A,B)$ is achieved
134601
whether they are complete metric space
59654
Show that in a discrete metric space, every subset is both open and closed.
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
96074
A net $\varphi : [0, \omega_1) \to M$ on a metric space $M$ converges $\iff \varphi$ is eventually constant
50677
Is this metric space incomplete?
73469
Continuity of the function $x\mapsto d(x,A)$ on a metric space
119247
Let $(M,d)$ be a compact metric space and $f:M \to M$ such that $d(f(x),f(y)) \ge d(x,y) , \forall x,y \in M$ , then $f$ is isometry?
158569
Proving a particular subset of $R^n$ is closed
69528
Metrizability of quotient spaces of metric spaces
90628
The metric spaces are Tychonoff spaces
26547
Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space
125610
Space of bounded continuous functions is complete