Showing that $(S,d)$ is a metric space for $S = (0,1]$ and $d(x,y) = |1/x - 1/y|$
16060
Showing this metric space is complete
43535
show that the interval of the form $[0,a)$ or $(a, 1]$ is open set in metric subspace $[0,1]$ but not open in $\mathbb R^1$
24266
Accumulation points of the set $S=\{(\frac {1} {n}, \frac {1} {m}) \space m, n \in \mathbb N\}$
85242
Deciding whether two metrics are topologically equivalent in the space $C^1([0,1])$
95783
Fixed points of contractions in metric spaces
36566
Equivalence classes and metric spaces
128897
Bounded sequence in a metric space
140692
Existence of a complete metric on $(0,1)$
66550
Cardinality of separable metric spaces
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
55016
Prove that if ($d(x,y)=0$ iff $x=y$) and if $d(x,z)\leq d(x,y)+d(z,y)$ then $d$ is a metric
134492
Proving that a Hölder space is a Banach space
94438
Show that the countable product of metric spaces is metrizable
132491
How to show that $C=C[0,1]$ is a Banach space
18040
Show that a compact metric space is bounded
27517
Isometry in compact metric spaces
49721
Prove the empty set is closed for a metric space (X,d).