Let $A \subset X$ metric space. Then $d(x,A) = 0$ if and only if $x\in \overline{A}?$
49374
Closure of a subset in a metric space
144400
Are compact subsets of metric spaces closed and bounded?
157753
Show that any set in a metric space can be written as the intersection of open sets
3072
If the empty set is a subset of every set, why isn't $\{\emptyset,\{a\}\}=\{\{a\}\}$?
26547
Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space
98553
Infinite metric space has open set $U$ which is infinite and its complement is infinite
125580
Proving that every countable metric space is disconnected?
858
Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?
137881
A not complete metric space?
93157
If $A \subseteq B$, does $\mbox{dist}(x,\partial A) \le \mbox{dist}(x, \partial B)$ hold for all $x \in A$
11114
Is a closed subset of a compact set (which is a subset of a metric space $M$) compact?
102457
for any $A\subseteq X$, $f(\overline{A})\subseteq\overline{f(A)}$ , if and only if $f: X \to Y$ is continuous.
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
28804
No. of possible dense subsets of a metric space
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
35631
$H_0(X,A) = 0 \iff A \cap X_i \neq \emptyset \forall $ path-components $X_i$