%0 Journal Article
%T Lebesgue Measurability of Separately Continuous Functions and Separability
%A V. V. Mykhaylyuk
%J International Journal of Mathematics and Mathematical Sciences
%D 2007
%I Hindawi Publishing Corporation
%R 10.1155/2007/54159
%X A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y, separately continuous function f:X×Y→ℝ and open set I⊆ℝ, the set f−1(I) is an Fσ-set) is studied. We show that every completely regular Baire space with the L-property and the countable chain condition is separable and constructs a nonseparable completely regular space with the L-property and the countable chain condition. This gives a negative answer to a question of M. Burke.
%U http://www.hindawi.com/journals/ijmms/2007/054159/abs/