Every separable metric space has cardinality less than or equal to the cardinality of the continuum.
66550
Cardinality of separable metric spaces
14972
Cardinality of Vitali sets: countably or uncountably infinite?
94438
Show that the countable product of metric spaces is metrizable
10513
What is the significance of the term "separable" in the context of countability properties?
125580
Proving that every countable metric space is disconnected?
272
Cantor Sets/nonempty/cardinality
49147
Showing that the class of all sets of a particular cardinality is not a set.
144731
Disjoint closed sets in a second countable zero-dimensional space can be separated by a clopen set
123061
$X$ metric separable then $C(X)$ separable
109054
Given an infinite set of cardinality $X$, is there a chain in $\mathcal P(X)$ of the same cardinalty of $\mathcal P(X)$?
53429
In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable?
95831
Compactness and sequential compactness in metric spaces
156783
$\mathbb R$ has the same cardinality of any interval
83518
Proving Two sets have same cardinality
35043
Cardinality of a set A is strictly less than the cardinality of the power set of A
17842
Is every set in a separable metric space the union of a perfect set and a set that is at most countable?
118390
Symbol for the cardinality of the continuum