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Separate continuity, joint continuity and the Lindelöf property

Author(s): Petar S. Kenderov; Warren B. Moors
Journal: Proc. Amer. Math. Soc. 134 (2006), 1503-1512.
MSC (2000): Primary 54C05, 22A10; Secondary 54E52, 39B99
Posted: December 14, 2005
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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
Email: pkend@math.bas.bg, vorednek@yahoo.com

Warren B. Moors
Affiliation: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
Email: moors@math.auckland.ac.nz

DOI: 10.1090/S0002-9939-05-08499-6
PII: S 0002-9939(05)08499-6
Keywords: Separate continuity, joint continuity, Lindel\" of property
Received by editor(s): July 27, 2004
Posted: 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
Copyright of article: Copyright 2005, American Mathematical Society

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