Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-08T04:24:28.380Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuous bijections on manifolds

Published online by Cambridge University Press:  09 April 2009

P. H. Doyle  and
J. G. Hocking
P. H. Doyle
Affiliation:
Department of Mathematics, Michigan State University, Wells Hall, East Lansing,Michigan 48824, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

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.

The main results of the paper give necessary and sufficient conditions as well as sufficient conditions that continuous bijections of a manifold onto itself be homeomorphisms. Such conditions include the embedding of manifolds, preserving ends, preserving closed half-rays and restrictions on boundary components. A number of counterexamples are given to likely conjectures.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 3 , November 1976 , pp. 257 - 263
Copyright
Copyright © Australian Mathematical Society 1976

References

Doyle, P. H. and Hocking, J. G. (1962), ‘A decomposition theorem for n–dimensional manifolds,’ Proc. Amer. Math. Soc. 13, 469–471.Google Scholar
Kuratowski, K. (1968), ‘Topology,’ (Vol. 2, Academic Press).Google Scholar
Pettey, Dix H. (1970), ‘One-to-one mappings into a plane,’ Fund. Math. 67, 209–218.CrossRefGoogle Scholar
Rajogopalan, M. and Wilkansky, A. (1966), ‘Reversible topological spaces,’ J. Austral. Math. Soc. 6, 129–138CrossRefGoogle Scholar