Does there exist a metric space $(X,d)$ such that for subsets $A$ and $B$, define $ d(A,B)= inf \{d(a,b): a \in A, b \in B \}$
5323
Example to show the distance between two closed sets can be 0 even if the two sets are disjoint
78108
Do these define metrics on $\mathbb{R}$?
55661
Existence of two disjoint closed sets with zero infimal distance
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
152057
Let $(X,d)$ be a compact metric space. Let $f: X \to X$ be such that $d(f(x),f(y)) = d(x,y)$ for all $x,y \in X$. Show that $f $ is onto (surjective).
146967
Understanding equivalent metric spaces
72950
Book recommendation for Metric Spaces
146485
Prove that the product space is a metric space.
140668
Union of $2$ set $A, B$ where $ A$ is a subset of $B$
7402
Showing a compact metric space has a countable dense subset
111119
Distance between any two points in a compact metric space
113688
Is Topological Space a Metric Space?
144360
For any sets $A$ and $B$, show that $(B\smallsetminus A)\cup A=B \iff A\subseteq B$.
28804
No. of possible dense subsets of a metric space
140124
The distance function on a metric space
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
142414
Generalization of metric spaces?