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Separate continuity, joint continuity and the Lindelöf property

Authors: Petar S. Kenderov and Warren B. Moors
Journal: Proc. Amer. Math. Soc. 134 (2006), 1503-1512
MSC (2000): Primary 54C05, 22A10; Secondary 54E52, 39B99
Published electronically: December 14, 2005
MathSciNet review: 2199199
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Abstract: In this paper we prove a theorem more general than the following. Suppose that $ X$ is Lindelöf and $ \alpha$-favourable and $ Y$ is Lindelöf and Cech-complete. Then for each separately continuous function $ f:X\times Y \rightarrow \mathbb{R}$ there exists a residual set $ R$ in $ X$ such that $ f$ is jointly continuous at each point of $ R\times Y$.

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Additional Information

Petar S. Kenderov
Affiliation: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
Address at time of publication: Institute of Mathematics, Bulgarian Academy of Science, Acad G. Bonchev Street, Block 8, 1113 Sofia, Bulgaria

Warren B. Moors
Affiliation: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand

Keywords: Separate continuity, joint continuity, Lindel\" of property
Received by editor(s): July 27, 2004
Published electronically: December 14, 2005
Additional Notes: The second author was supported by the Marsden Fund research grant, UOA0422, administered by the Royal Society of New Zealand
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society

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