Fixed points of subopen multifunctions

Fixed points of subopen multifunctions
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by J. F. McClendon PDF

Proc. Amer. Math. Soc. 84 (1982), 425-428 Request permission

A fixed point theorem of the Lefschetz type is proved for subopen (e.g., open-graph) multifunctions. A coincidence version is also given.

References

Karol Borsuk, Theory of retracts, Monografie Matematyczne, Tom 44, Państwowe Wydawnictwo Naukowe, Warsaw, 1967. MR 0216473
Robert F. Brown, The Lefschetz fixed point theorem, Scott, Foresman & Co., Glenview, Ill.-London, 1971. MR 0283793
Samuel Eilenberg and Deane Montgomery, Fixed point theorems for multi-valued transformations, Amer. J. Math. 68 (1946), 214–222. MR 16676, DOI 10.2307/2371832
Brayton Gray, Homotopy theory, Pure and Applied Mathematics, Vol. 64, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. An introduction to algebraic topology. MR 0402714
Andreu Mas-Colell, A selection theorem for open graph correspondences with star-shaped values, J. Math. Anal. Appl. 68 (1979), no. 1, 273–275. MR 531437, DOI 10.1016/0022-247X(79)90114-8
J. F. McClendon, Note on a selection theorem of Mas-Colell, J. Math. Anal. Appl. 77 (1980), no. 1, 326–327. MR 591280, DOI 10.1016/0022-247X(80)90279-6

Subopen multifunctions and selections

Ernest Michael, Continuous selections. III, Ann. of Math. (2) 65 (1957), 375–390. MR 83715, DOI 10.2307/1969969
Ernest Michael, Convex structures and continuous selections, Canadian J. Math. 11 (1959), 556–575. MR 109344, DOI 10.4153/CJM-1959-051-9
Michael J. Powers, Multi-valued mappings and Lefschetz fixed point theorems, Proc. Cambridge Philos. Soc. 68 (1970), 619–630. MR 264657, DOI 10.1017/s030500410007660x
Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112