Infimum of a metric is continuous
111561
Distance of a point to a subset.
71487
Real Analysis: Continuity of a Composition Function
96074
A net $\varphi : [0, \omega_1) \to M$ on a metric space $M$ converges $\iff \varphi$ is eventually constant
46834
show that a distance function is continuous
10747
Given function $g$ continuous in line $[0,\infty)$...
70106
diameter on a compact metric space
131992
A problem on continuous functions
14578
Proving that an additive function $f$ is continuous if it is continuous at a single point
62479
A isometric map in metric space is surjective?
17223
Continuity of an inverse function.
44574
Continuity of absolute value of a function
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
142459
Continuity of a Function in Terms of Closure and Interior
153952
A map between metric spaces preserving convergent sequences is continuous
87536
Supremum of the infimum
154572
Continuity of a function at an isolated point
127114
Differentiability implying continuity