Hostname: page-component-77c89778f8-rkxrd Total loading time: 0 Render date: 2024-07-17T01:47:40.560Z Has data issue: false hasContentIssue false
  • English
  • Français

Multi-valued mappings and Lefschetz fixed point theorems

Published online by Cambridge University Press:  24 October 2008

Michael J. Powers
Michael J. Powers
Affiliation:
Northern Illinois University, DeKalb, Illinois 60115, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

By a multi-valued map from a space X to a space Y we mean a map which assigns to each point x in X a non-empty subset F(x) of Y. When X = Y, a point x in X is a fized point for F if x is in F(x).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 3 , November 1970 , pp. 619 - 630
Copyright
Copyright © Cambridge Philosophical Society 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Begle, E. G.The Vietoris mapping theorem for bicompact spaces. Ann. of Math. 51 (1950), 534–543.CrossRefGoogle Scholar
(2)Begle, E. G.The Vietoris mapping theorem for bicompact spaces II. Michigan Math. J. 3 (1955–1956), 179–180.CrossRefGoogle Scholar
(3)Browder, F. E.On a generalization of the Schauder fixed point theorem. Duke Math. J. 26 (1959), 291–303.CrossRefGoogle Scholar
(4)Browder, F. E.Fixed point theorems on infinite dimensional manifolds. Trans. Amer. Math. Soc. 119 (1965), 179–194.CrossRefGoogle Scholar
(5)Eilenberg, S. and Montgomery, D.Fixed point theorems for multi-valued transformations. Amer. J. Math. 58 (1946), 214–222.CrossRefGoogle Scholar
(6)Eileberg, S. and Steenrod, N.Foundations of algebraic topology (Princeton Univ. Press, Princeton, N.J., 1952).CrossRefGoogle Scholar
(7)Hu, S.-T.Theory of retracts (Wayne State Univ. Press, Detroit, 1965).Google Scholar
(8)Jaworowski, J. W. and Powers, M. J.A-spaces and fixed point theorems. Fund. Math. 64 (1969), 157–162.CrossRefGoogle Scholar
(9)Leray, J.Theorie des Points Fixes: Indice Total et Nombre de Lefschetz. Bull. Soc. Math. France 87 (1959), 221–233.Google Scholar
(10)Powers, M. J. Multi-valued mappings and fixed point theorems, Ph.D. Thesis, Indiana University, 1968.Google Scholar
(11)Spanier, E. H.Algebraic topology (McGraw-Hill, New York, 1966).Google Scholar