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A note on spaces related to Namioka spaces

Published online by Cambridge University Press:  17 April 2009

J.P. Lee  and
Z. Piotrowski
J.P. Lee
Affiliation:
Department of Mathematics, State University of New York/College at Old Westbury, Box 210, Old Westbury, Long Island, New York 11568, USA;
Z. Piotrowski
Affiliation:
Department of Mathematical and Computer Sciences, Youngstown State University, Youngstown, Ohio 44555, USA.
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Abstract

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Namioka proved that the following condition (*) given below holds, if X is Čech-complete and Y is a locally compact, σ-compact space.

(*) Let X and Y be spaces, Z be a metric space and let f: X × Y → Z be separately continuous. Then there is a dense, Gδ set A in X such that A × Y ⊂ C(f).

Following Christensen a space X is called Namioka if (*) is true for any compact space Y. In this paper we introduce and study a new class of spaces which is closely related to Namioka spaces. Namely, we say that a space Y is co-Namioka if (*) holds for any Namioka space X.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 2 , April 1985 , pp. 285 - 292
Copyright
Copyright © Australian Mathematical Society 1985

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