# 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 LindelofTheorem 2014-11-06 13:45:28 2014-11-06 13:45:28 drini (3) pahio (2872) 7 drini (2872) Theorem msc 54D99 SecondCountable Lindelof