The Lindelöf number L(X) of a topological space X is the least infinite cardinal λ with the property that every open covering of X has a subcovering of cardinality at most λ. Prove that if evert non-countably infinite subset of a first countable space X has a point of condensation, then L(X)=supL(A), where A runs over the separable closed subspaces of X.
(A point of condensation of a subset H⊆X is a point x∈X such that any neighbourhood of x intersects H in a non-countably infinite set.) college contestsMiklos Schweitzertopology