Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-29T23:23:52.273Z Has data issue: false hasContentIssue false
  • English
  • Français

Topological degree of non-compact mappings

Published online by Cambridge University Press:  24 October 2008

J. G. Taylor
J. G. Taylor
Affiliation:
Department of Physics, Rutgers, The State University New Brunswick, New Jersey
Get access Rights & Permissions [Opens in a new window]

Abstract

We extend the notion of topological degree to a suitable class of continuous mappings of a locally convex Hausdorff topological vector space into itself which are not completely continuous. This extension and the resulting existence theorems for non-linear equations are further extended to product spaces. Our extension is developed with application to quantum field theory in mind; this application is made elsewhere.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 2 , April 1967 , pp. 335 - 347
Copyright
Copyright © Cambridge Philosophical Society 1967

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 AND NOTES

(1)Taylor, J. G.On the existence of field theory I: The analytic approach. J. Math. Phys. 7 (1966), 1720.Google Scholar
(2)Leray, J. and Schauder, J.Jopologie et equations fonctionelles. Ann. Sci. École Norm. Sup. 51 (1934), 45–78.CrossRefGoogle Scholar
(3)Röthe, E.The theory of topological order in some linear topological spaces. Iowa State College Journal of Science 13 (1939), 373–390.Google Scholar
(4)Nagumo, M.Degree of mapping in convex linear topological spaces. Amer. J. Math. 73 (1951), 497–511.Google Scholar
(5)Browder, F.On the fixed point index for continuous mappings of locally connected spaces. Summa Brasil. Math. 4 (1960), 253–293.Google Scholar
(6)Cronin, J.Fixed points and topological degree in non-linear analysis. Mathematical Surveys, no. 11, Amer. Math. Soc. 1964, Chapter 3, section 3.Google Scholar
(7)Taylor, J. G.A new class of integral equations and their existence. Rutgers University Preprint (1965).Google Scholar
(8)Krasnoselskii, M. A.Topological Methods in the Theory of Non-Linear Integral Equation, Theorem 4.1. (Pergamon Press, 1964.)Google Scholar
(9) I would like to thank Professor Jane Cronin for raising this question with me, and suggesting a method of theorem 1 in section 2.Google Scholar
(10)A c denotes the complement of the set A in E.Google Scholar
(11)Jaffe, A.The divergence of field theory. Commun. Math. Phys. 1 (1965), 217.CrossRefGoogle Scholar