Hostname: page-component-745bb68f8f-grxwn Total loading time: 0 Render date: 2025-02-04T19:46:34.620Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Bing, R. H., The elusive fixed point property, Amer. Math. Monthly 76 (1969), 119–131.Google Scholar
2. Borsuk, K., Theory of retracts (Warszawa 1967).Google Scholar
3. Hu, S. T., Homotopy theory (Academic Press, New York, 1959).Google Scholar
4. Hurewicz, W. and Wallman, H., Dimension theory (Princeton Univ. Press, Princeton 1941).Google Scholar
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
8. Young, G. S., Fixed point theorems for arcwise connected continua, Proc. Amer. Math. Soc. 11 (1960), 880–884.Google Scholar