Lebesgue Measurability of Separately Continuous Functions and Separability

V. V. Mykhaylyuk

International Journal of Mathematics and Mathematical Sciences, 2007, vol. 2007, 1-4

Abstract:

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 I ⊆ ℠, the set f − 1 ( I ) is an F σ -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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:054159

DOI: 10.1155/2007/54159

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