Closed iff sequentially closed in metric spaces and the Axiom of Countable Choice
56143
Proof of a basic $AC_\omega$ equivalence
109638
Show that a complete metric space without isolated points is uncountable
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
154978
Some equivalent formulations of compactness of a metric space
74877
Every metric space with a countable base is separable
112303
Distances between closed sets on metric spaces
82947
Undecidable cardinality
64260
Prove that a function between metric spaces is continuous iff the inverse image of a closed set is closed
81929
d-metrizable spaces are sequential
125580
Proving that every countable metric space is disconnected?
136851
Proof that the set of subsequential limits is closed
80276
Metric Space & Cauchy Sequence
49703
Analogue of closed graph theorem
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
35573
A closed ball in a metric space is a closed set
13848
Showing that if a subset of a complete metric space is closed, it is also complete
81509
The cardinality of a countable union of countable sets, without the axiom of choice