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Title: On $\delta $-continuous selections of small multifunctions and covering properties (English)
Author: Fedeli, Alessandro
Author: Pelant, Jan
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 32
Issue: 1
Year: 1991
Pages: 155-159
Category: math
Summary: The spaces for which each $\delta$-continuous function can be extended to a $2\delta$-small point-open l.s.c\. multifunction (resp. point-closed u.s.c\. multifunction) are studied. Some sufficient conditions and counterexamples are given. (English)
Keyword: $\delta $-continuous selections
Keyword: small multifunctions
Keyword: paracompactness
Keyword: orthocompactness
MSC: 54C60
MSC: 54C65
MSC: 54D18
MSC: 54D20
idZBL: Zbl 0734.54010
idMR: MR1118298
Date available: 2008-10-09T13:11:34Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Burke D.K.: Orthocompactness and perfect mappings.Proc. Amer. Math. Soc. 79 (1980), 484-486. Zbl 0433.54005, MR 0567998
Reference: [2] Burke D.K.: Covering properties.Chapter 9 of Handbook of set-theoretic topology, edited by K. Kunen and J.E. Vaughan, Elsevier Science Publishers, B.V., North Holland, 1984, 347-422. Zbl 0569.54022, MR 0776628
Reference: [3] Gruenhage G.: On closed images of orthocompact spaces.Proc. Amer. Math. Soc. 77 (1979), 389-394. Zbl 0422.54013, MR 0545602
Reference: [4] Klee V.: Stability of the fixed point theory.Colloq. Math. 8 (1961), 43-46. MR 0126261
Reference: [5] Muenzenberger T.B.: On the proximate fixed point property for multifunctions.Colloq. Math. 19 (1968), 245-250. Zbl 0181.26203, MR 0227968
Reference: [6] Schirmer H.: $\delta $-continuous selections of small multifunctions.Can. J. Math. XXIV, (4) (1972), 631-635. Zbl 0219.54012, MR 0300255
Reference: [7] Smithson R.E.: A note on $\delta $-continuity and proximate fixed points for multi-valued functions.Proc Amer. Math. Soc. 23 (1969), 256-260. Zbl 0183.27703, MR 0248774


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