MathDB

The Lindelöf number

L(X)

of a topological space

X

is the least infinite cardinal

\lambda

with the property that every open covering of

X

has a subcovering of cardinality at most

\lambda

. Prove that if evert non-countably infinite subset of a first countable space

X

has a point of condensation, then

L(X)=\sup L(A)

, where

A

runs over the separable closed subspaces of

X

. (A point of condensation of a subset

H\subseteq X

is a point

x\in X

such that any neighbourhood of

x

intersects

H

in a non-countably infinite set.)

Problem Statement