Namespaces
Variants
Actions

Difference between revisions of "Separable space"

From Encyclopedia of Mathematics
Jump to: navigation, search
m (links)
(MSC 54D65)
 
Line 1: Line 1:
 
{{TEX|done}}
 
{{TEX|done}}
 +
{{MSC|54D65}}
  
 
A [[topological space]] containing a [[Countable set|countable]] [[everywhere-dense set]].
 
A [[topological space]] containing a [[Countable set|countable]] [[everywhere-dense set]].

Latest revision as of 19:33, 12 December 2015

2020 Mathematics Subject Classification: Primary: 54D65 [MSN][ZBL]

A topological space containing a countable everywhere-dense set.

Comments

Thus, a space $X$ is separable if and only if its 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

[1] A.V. Arkhangel'skii, V.I. Ponomarev, "Fundamentals of general topology: problems and exercises" , Reidel (1984) pp. 43ff (Translated from Russian)
How to Cite This Entry:
Separable space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Separable_space&oldid=36897
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article