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International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 54159, 4 pages
Research Article

Lebesgue Measurability of Separately Continuous Functions and Separability

Department of Mathematical Analysis, Chernivtsi National University, Kotsjubyns'koho 2, Chernivtsi 58012, Ukraine

Received 4 September 2006; Accepted 22 April 2007

Academic Editor: Peter Johnson

Copyright © 2007 V. V. Mykhaylyuk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 and open set Iℝ, the set f1(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.