Uniformly equivalent metrics
127034
Let $\rho(x,y)= \frac{d(x,y)}{1+d(x,y)}$, show that $\rho$ is a metric equivalent to $d$
126944
Metric spaces problem
150987
Showing that the product and metric topology on $\mathbb{R}^n$ are equivalent
70409
Rational Equivalence Relation and Measure
6785
Equicontinuity on a compact metric space turns pointwise to uniform convergence
52252
Equivalent definitions of isometry
92005
Existence of compact/complete metric on countable set
37924
Equivalence of norms proof
74607
Variation of the metric with respect to the metric
18942
An equivalent definition of uniform integrability
135315
Proving whether a function on the set of real sequences is a metric
11773
Levi-Civita connection between conformal metrics
87086
Equivalence of convergence in products of sequences.
90110
Hyperbolic metric geodesically complete
72950
Book recommendation for Metric Spaces
143951
Can we determine uniform continuity from graphs?
42266
Show that $d(x,y)=\min \{1,|x-y|\}$ is a metric on $\mathbb R$