View source for Separable space

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{{MSC|54D65}}

A [[topological space]] containing a [[Countable set|countable]] [[everywhere-dense set]].

====Comments====
Thus, a space $X$ is separable if and only if its [[Density (of a topological space)|density]] $d(X)\leq\aleph_0$; cf. [[Cardinal characteristic]].

A [[metrizable space]] is separable if and only if it satisfies the [[Second axiom of countability]].

====References====
<table>
<TR><TD valign="top">[1]</TD> <TD valign="top">  A.V. Arkhangel'skii,   V.I. Ponomarev,   "Fundamentals of general topology: problems and exercises" , Reidel  (1984)  pp. 43ff  (Translated from Russian)</TD></TR></table>