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Pseudonormality and starcompactness of $\sigma$-products


Author: Keiko Chiba
Journal: Proc. Amer. Math. Soc. 131 (2003), 319-327
MSC (2000): Primary 54B05, 54B10, 54D15, 54D20
Published electronically: May 8, 2002
MathSciNet review: 1929052
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Abstract: In this paper we shall prove the following: For every non-trivial $\sigma$-product $\sigma$, of uncountable number of spaces, having at least two points, $\sigma \smallsetminus \sigma_{n}$ is not pseudonormal. And every non-trivial $\sigma$-product is not strongly starcompact.


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Additional Information

Keiko Chiba
Affiliation: Department of Mathematics, Faculty of Science, Shizuoka University, Ohya, Shizuoka, 422-8529 Japan
Email: smktiba@ipc.shizuoka.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06496-1
Keywords: $\sigma$-product, pseudonormal, strongly starcompact, starcompact
Received by editor(s): April 20, 2001
Received by editor(s) in revised form: August 20, 2001
Published electronically: May 8, 2002
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society