About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Fedeli, Alessandro ; Pelant, Jan
On $\delta $-continuous selections of small multifunctions and covering properties. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 32 (1991), issue 1, pp. 155-159
MSC: 54C60, 54C65, 54D18, 54D20 | MR 1118298 | Zbl 0734.54010
Keywords:
$\delta $-continuous selections; small multifunctions; paracompactness; orthocompactness
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.
References:
[1] Burke D.K.: Orthocompactness and perfect mappings. Proc. Amer. Math. Soc. 79 (1980), 484-486. MR 0567998 | Zbl 0433.54005
[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. MR 0776628 | Zbl 0569.54022
[3] Gruenhage G.: On closed images of orthocompact spaces. Proc. Amer. Math. Soc. 77 (1979), 389-394. MR 0545602 | Zbl 0422.54013
[4] Klee V.: Stability of the fixed point theory. Colloq. Math. 8 (1961), 43-46. MR 0126261
[5] Muenzenberger T.B.: On the proximate fixed point property for multifunctions. Colloq. Math. 19 (1968), 245-250. MR 0227968 | Zbl 0181.26203
[6] Schirmer H.: $\delta $-continuous selections of small multifunctions. Can. J. Math. XXIV, (4) (1972), 631-635. MR 0300255 | Zbl 0219.54012
[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. MR 0248774 | Zbl 0183.27703
Partner of
EuDML logo