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On a 1-Dimensional Planar Continuum without the Fixed Point Property

Published online by Cambridge University Press:  20 November 2018

John R. Martin
John R. Martin*
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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In [5 ; 6] the author considers the following two problems posed by Professor Lloyd Tucker.

Problem 1. Does there exist a 1-dimensional continuum X without the fixed point property such that every retract of X has the fixed point property with respect to one-to-one maps?

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1300 - 1303
Copyright
Copyright © Canadian Mathematical Society 1977

References

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5. Martin, J. R., On 1-dimensional continua without the fixed point property, Colloq. Math. 31 (1974), 203–205.Google Scholar
6. Martin, J. R. On a simply connected 1-dimensional continuum without the fixed point property, Fund. Math. 91 (1976), 179–182.Google Scholar
7. Mohler, L., The fixed point property for homeomorphisms of 1-arcwise connected continua, Proc. Amer. Math. Soc. 52 (1975), 451–456.Google Scholar
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