International Journal of Mathematics and Mathematical Sciences
Volume 2007 (2007), Article ID 54159, 4 pages
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 -property (a topological space has -property if for every topological space , separately continuous function and open set the set is an -set) is studied. We show that every completely
regular Baire space with the -property and the countable chain condition is separable and constructs a nonseparable completely regular space with the -property and the countable chain condition. This gives a negative answer to a question of M. Burke.