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Coverings of products of linear topological spaces

Published online by Cambridge University Press:  09 April 2009

Aaron R. Todd
Aaron R. Todd
Affiliation:
Division of Mathematics and Science St John's University, Staten Island Campus Staten Island, New York 10301, U.S.A.
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Abstract

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An extension of the Banach-Mackey theorem is used to prove a theorem about countable families of closed balanced convex sets that cover a product of linear topological spaces. This theorem clarifies proofs that certain Baire-type properties, including the unordered Baire-like property, are preserved under products. A modification of the theorem is used to show that a property involving the bounded-absorbing sequences of DeWilde and Houet is also productive. Finally, a question is posed about balanced absorbing sets relating to products of linear Baire spaces.

1980 Mathematics subject classification (Amer. Math. Soc.): 46 A 99.

Keywords

Bairelocally convexunordered Baire-like.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 3 , May 1980 , pp. 281 - 290
Copyright
Copyright © Australian Mathematical Society 1980

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