Is every metric space with countable base a separable metric space?
74877
Every metric space with a countable base is separable
7723
Countable basis of function spaces
151984
Proving the existence of a metric space
48174
Are countable topological spaces second-countable?
36566
Equivalence classes and metric spaces
127166
Specific example of a space that is separable but not second countable.
70106
diameter on a compact metric space
64375
Non-Metrizable Topological Spaces
118508
Is the axiom of choice needed in proving that metric spaces in which every infinite subset has a limit point are compact?
13848
Showing that if a subset of a complete metric space is closed, it is also complete
99816
Existence of Topologically Transitive Maps on nice Metric Spaces
149426
Is there a Hausdorff space $X$ separating points of any Hausdorff space?
50677
Is this metric space incomplete?
16892
Reference request: product Borel $\sigma$-algebra of non-separable metric spaces
6523
Prove that the space has a countable dense subset
124179
Proof that every metric space is normal
154978
Some equivalent formulations of compactness of a metric space