Lindelöf theorem

If a topological space $(X,\tau )$ satisfies the second axiom of countability, and if $A$ is any subset of $X$, then any open cover for $A$ has a countable subcover.

In particular, we have that $(X,\tau )$ is a Lindelöf space (http://planetmath.org/lindelofspace).

Title	Lindelöf theorem
Canonical name	LindelofTheorem
Date of creation	2014-11-06 13:45:28
Last modified on	2014-11-06 13:45:28
Owner	drini (3)
Last modified by	pahio (2872)
Numerical id	7
Author	drini (2872)
Entry type	Theorem
Classification	msc 54D99
Related topic	SecondCountable
Related topic	Lindelof