A topological space containing a countable everywhere-dense set.
Thus, a space is separable if and only if its density ; cf. Cardinal characteristic.
A metrizable space is separable if and only if it satisfies the second axiom of countability.
|||A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) pp. 43ff (Translated from Russian)|
Separable space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Separable_space&oldid=11352