Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-12-01T02:32:42.636Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Adasch, N. (1970), ‘Topologische Produkte gewisser topologisher Vektorräume’, Math. Ann. 189, 280–284.CrossRefGoogle Scholar
Bourbaki, N. (1948), Topologie générale, Chapter 9 (Act. Sci. Ind. No. 1045, Hermann, Paris).Google Scholar
DeWilde, M. and Houet, C. (1971), ‘On increasing sequences of absolutely convex sets in locally convex spaces’, Math. Ann. 192, 257–261.CrossRefGoogle Scholar
Horv´th, J. (1966), Topological vector spaces and distributions, Vol. 1 (Addison-Wesley, Reading, Mass.).Google Scholar
Kelley, J. L., Namioka, I. et al. (1963), Linear topological spaces (D. Van Nostrand, Princeton, New Jersey).CrossRefGoogle Scholar
Mazur, S. and Orlicz, W. (1948), ‘Sur les espaces métriques linéaires I’, Studia Math. 10, 184–208.CrossRefGoogle Scholar
Oxtoby, J. C. (1961), ‘Cartesian products of Baire spaces’, Fund. Math. 49, 157–266.CrossRefGoogle Scholar
Robertson, W. (1958), ‘Completions of topological vectors spaces’, Proc. London Math. Soc. (3) 8, 242–257.CrossRefGoogle Scholar
Saxon, S. (1974a), ‘Some normed barrelled spaces which are not Baire’, Math. Ann. 209, 153–160.CrossRefGoogle Scholar
Saxon, S. (1974b), ‘Two characterizations of linear Baire spaces’, Proc. Amer. Math. Soc. 45, 204–208.CrossRefGoogle Scholar
Todd, A. R. and Saxon, S. A. (1973), ‘A property of locally convex Baire spaces’, Math. Ann. 206, 23–34.CrossRefGoogle Scholar