Separable metric space spanned by base
67050
Every separable metric space has a countable base
31686
Every metric space can be isometrically embedded in a Banach space, so that it's a linearly independent set
35156
Constructing a choice function in a complete & separable metric space
73154
Compact subset in colimit of spaces
27517
Isometry in compact metric spaces
9775
Metric on Cartesian Product
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
17842
Is every set in a separable metric space the union of a perfect set and a set that is at most countable?
116069
Is every metric space a subspace of some connected metric space?
35652
Every compact metric space is complete
18040
Show that a compact metric space is bounded
28804
No. of possible dense subsets of a metric space
132641
Proving that Euclidean Space is a complete metric space
81929
d-metrizable spaces are sequential
11455
Connected metric spaces with at least 2 points are uncountable.
125580
Proving that every countable metric space is disconnected?
143484
A separable locally compact metric space is compact iff all of its homeomorphic metric spaces are bounded