Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T02:11:37.422Z Has data issue: false hasContentIssue false
  • English
  • Français

A WEAKLY ANALYTIC LOCALLY CONVEX SPACE WHICH IS NOT K-ANALYTIC

Part of: Connections with other structures, applications Topological linear spaces and related structures Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  09 February 2009

JUAN CARLOS FERRANDO
JUAN CARLOS FERRANDO*
Affiliation:
Centro de Investigación Operativa, Universidad Miguel Hernández, 03202 Elche, Alicante, Spain (email: [email protected])
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.

It is shown that the dual of the space Cp(I) of all real-valued continuous functions on the closed unit interval with the pointwise topology, when equipped with the Mackey topology, is a non K-analytic but weakly analytic locally convex space.

Keywords

analytic and K-analytic spacelocally convex spaceBorel measure

MSC classification

Secondary: 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 46A03: General theory of locally convex spaces 54C35: Function spaces
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 1 , February 2009 , pp. 31 - 35
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This research has been partially supported by project MTM2005-01182 of the Spanish Ministry of Education and Science, co-financed by the European Community (Feder funds).

References

[1] Arkhangel’skii, A. V., Topological Function Spaces, Mathematics and its Applications, 78 (Kluwer Academic Publishers, Dordrecht, Boston, London, 1992).Google Scholar
[2] Ka̧kol, J., López Pellicer, M. and Śliwa, W., Weakly K-analytic spaces and the three-space property for analyticity, submitted.Google Scholar
[3] Nakamura, M., ‘On quasi-Souslin space and closed graph theorem’, Proc. Japan. Acad. 46 (1970).Google Scholar
[4] Rogers, C. A., ‘Analytic sets in Hausdorff spaces’, Mathematika 11 (1968), 1–8.CrossRefGoogle Scholar
[5] Talagrand, M., ‘Espaces de Banach faiblement K-analytiques’, Ann. of Math. 110 (1979), 407–438.Google Scholar
[6] Valdivia, M., Topics in Locally Convex Spaces, North Holland Mathematics Studies, 67 (North Holland, Amsterdam, 1982).Google Scholar