Showing that the following metric space is complete
52104
A pseudometric on the space of the measurable functions is complete
105437
How can I show these two metrics give the same topology?
138607
Proof that a limit point compact metric space is compact.
153952
A map between metric spaces preserving convergent sequences is continuous
26547
Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space
146485
Prove that the product space is a metric space.
128598
How to prove this is a metric?
73469
Continuity of the function $x\mapsto d(x,A)$ on a metric space
95783
Fixed points of contractions in metric spaces
42638
Showing that a function $f$ has a unique fixed point in a metric space.
27652
metric on the Euclidean Group
157753
Show that any set in a metric space can be written as the intersection of open sets
141643
Showing $\rho (x,y)=\frac{d(x,y)}{1+d(x,y)}$ is a metric
119105
If $(X,d)$ is a complete metric space and $A$ is closed then show that for $x \in X$ there exists an element $a_0 \in A$ such that $d(x,A)=d(x,a_0)$
123061
$X$ metric separable then $C(X)$ separable
69777
Show that, for every metric $d$, the metrics $d/(1+d)$ and $\min\{1,d\}$ are equivalent
72033
Is this proof sufficient to show that a concave function of a metric is also a metric?