Separable $\Rightarrow$ Lindelöf for metric spaces without using second-countability
105815
Does proving (second countable) $\Rightarrow$ (Lindelöf) require the axiom of choice?
34298
sequentially continuous on a non first-countable
105791
Does separability imply the Lindelöf property?
128897
Bounded sequence in a metric space
90628
The metric spaces are Tychonoff spaces
13848
Showing that if a subset of a complete metric space is closed, it is also complete
107701
Show that a connected metric space is $\epsilon$-chainable for $\epsilon>0$
134601
whether they are complete metric space
26563
Help completing a proof regarding an infinite family of nested closed subsets in a compact metric space
147961
Characterizing simply connected spaces
33859
How to show that a disjoint sum of metric spaces is metrizable?
153651
Countable partition in atoms
136094
$G_\delta$ singletons in compact Hausdorff and first countability
106670
Existence of vector space complement and axiom of choice
127678
A partition of the unit interval into uncountably many dense uncountable subsets
11383
Disjoint compact sets in a Hausdorff space can be separated
126759
Unbounded continuous function on non-compact metric space