A fixed point theorem for the pseudo-circle |
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| Authors: | J.P. Boroński |
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| Affiliation: | a Department of Mathematics, Auburn University at Montgomery, P.O. Box 244023, Montgomery, AL 36124, United States
b Faculty of Applied Mathematics, AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland |
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| Abstract: | Let f:C→C be a self-map of the pseudo-circle C. Suppose that C is embedded into an annulus A, so that it separates the two components of the boundary of A. Let F:A→A be an extension of f to A (i.e. F|C=f). If F is of degree d then f has at least |d−1| fixed points. This result generalizes to all plane separating circle-like continua. |
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| Keywords: | primary, 54F15, 54H25 secondary, 54H20 |
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