Hostname: page-component-77c89778f8-sh8wx Total loading time: 0 Render date: 2024-07-17T16:48:50.096Z Has data issue: false hasContentIssue false
  • English
  • Français

Almost Baire class one multi-functions

Published online by Cambridge University Press:  17 April 2009

P. Maritz
P. Maritz
Affiliation:
Department of Mathematics, University of Stellenbosch, Stellenbosch 7600, South Africa
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.

In this paper we employ quasi-continuous multifunctions and introduce almost Baire class 1 multifunctions in order to generalize a theorem of Kuratowski and also to answer a question posed by him concerning Baire class 1 multifunctions. We also show that certain multifunctions can be decomposed into mutually singular multifunctions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 34 , Issue 2 , October 1986 , pp. 297 - 308
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Berge, C., Topological spaces (Oliver and Boyd, Edinburgh-London, 1st English edition, 1963).Google Scholar
[2]Čech, E., Topological spaces (Interscience Publishers, John Wiley, London, revised edition, 1966).Google Scholar
[3]Crossley, S. G. and Hildebrand, S. K., “Semi-closure” Tex. J. Sci. 22 (1971), 99–112.Google Scholar
[4]Ewert, J. and Lipski, T., “Quasi-continuous multivalued mappings”, Math. Slovaca 33 (1983), 69–74.Google Scholar
[5]Kenderov, P.S., “Continuity-like properties of set-valued mapping”, Serdica 9 (1983), 149–160.Google Scholar
[6]Kuratowski, K., Topology, volume I (Academic Press, New York, San Francisco, London, new edition, 1966).Google Scholar
[7]Kuratowski, K., Topology, volume II (Academic Press, New York, London, new edition, 1968).Google Scholar
[8]Kuratowski, K., “Some problems concerning semi-continuous set-valued mapping”, Proc. Conf. at Buffalo, May 8–10, 1969 (Lecture Notes in Mathematics 171 Springer-Verlag, Berlin, Heidelberg, New York, 1970).Google Scholar
[9]Levine, N., “Semi-open sets and semi-continuity in topological spaces”, Amer. Math. Monthly 70 (1963), 36–41.CrossRefGoogle Scholar
[10]Michael, E., “Topologies on spaces of subsets”, Trans. Amer. Math. Soc. 71 (1951), 152–182.Google Scholar
[11]Oxtoby, J.C., Measure and category (Graduate Texts in Mathematics 2 Springer-Verlag, New York, Heidelberg, Berlin, 2nd edition, 1980).Google Scholar
[12]Steen, L.A. and Seebach, J.A. Jr., Counterexamples in topology (Springer-Verlag, New York, Heidelberg, Berlin, 2nd edition, 1978).Google Scholar
[13]Zaanen, A.C., Integration (North-Holland, Amsterdam, 1967).Google Scholar