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A fixed-point theorem for $UV^n$ usco maps

Author(s): Valentin G. Gutev
Journal: Proc. Amer. Math. Soc. 124 (1996), 945-952.
MSC (1991): Primary 54H25, 54C60; Secondary 54B15
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Abstract: The familiar fixed-point theorem of Kakutani is strengthened by weakening the hypotheses on the set-valued mapping. Applications are made for $UV^n$ and $UV^\omega$ decompositions of compact metric spaces.

References:

1.: J. Cobb and W. Voxman, Some fixed point results for decompositions of compact metric spaces, Proc. Amer. Math. Soc., 33 (1972), 156--160. MR 44:7524
2.: A. H. Dranishnikov, Absolute extenzors in dimension and -soft mappings raising dimension (in Russian), Uspehi Mat. Nauk, 39 (1984), pp. 55--95. MR 86c:54017
3.: S. Kakutani, A generalization of Brouwer's fixed point theorem, Duke Math. J., 8 (1941), 457--459. MR 3:60c
4.: E. Michael, Continuous selections II, Ann. of Math., 64 (1956), 562--580. MR 18:325e

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Additional Information:

Valentin G. Gutev
Affiliation: Department of Mathematics, University of Sofia, Sofia, Bulgaria
Address at time of publication: Institute of Mathematics, Bulgarian Academy of Sciences, 1090 Sofia, Bulgaria
Email: gutev@bgcict.acad.bg, gutev@fmi.uni-sofia.bg

DOI: 10.1090/S0002-9939-96-03491-0
PII: S 0002-9939(96)03491-0
Keywords: Set-valued mapping, upper semi-continuous, $UV^n$ set, decomposition
Received by editor(s): September 10, 1993
Additional Notes: This research was supported in part by NSF at the Bulgarian Ministry of Science and Education under grant MM-420/94.
Communicated by: James E. West
Copyright of article: Copyright 1996, American Mathematical Society


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