Continuity of metric
73469
Continuity of the function $x\mapsto d(x,A)$ on a metric space
20164
Is there always an equivalent metric which is not complete?
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$
118048
Can a function with just one point in its domain be continuous?
45276
Continuous map on $S^2$
144353
A closed ball in a metric space is closed
60521
Continuity of a convex function
83159
Defining a metric space
112303
Distances between closed sets on metric spaces
98772
Continuity of a function in $\mathbb{R}$
154978
Some equivalent formulations of compactness of a metric space
27652
metric on the Euclidean Group
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
59519
What about the continuity of these functions in the uniform topology?
153952
A map between metric spaces preserving convergent sequences is continuous
92005
Existence of compact/complete metric on countable set
70106
diameter on a compact metric space