Does a separable metric space have a countable basis?
119649
Every metrizable space with a countable dense subset has a countable basis
49563
Cauchy nets in a metric space
123061
$X$ metric separable then $C(X)$ separable
17067
To prove that $(\mathbb{P(N)},d)$ is a metric space
7069
On the product of $\mathfrak c$-many separable spaces
36566
Equivalence classes and metric spaces
68230
The cardinality of a countable union of sets with less than continuum cardinality
22295
Subspace of a separable space is separable
94438
Show that the countable product of metric spaces is metrizable
4111
Outer measure is countably subadditive
33859
How to show that a disjoint sum of metric spaces is metrizable?
107701
Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
128118
Is the cofinite topology on a countable set first countable?
80276
Metric Space & Cauchy Sequence
99478
countably infinite union of countably infinite sets is countable
157565
Is every dense subspace of a separable space separable?
15480
Open set in a metric space is union of closed sets