Hostname: page-component-5c6d5d7d68-wpx84 Total loading time: 0 Render date: 2024-08-25T21:24:40.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Strongly reversible manifolds

Part of: Topological manifolds

Published online by Cambridge University Press:  09 April 2009

J. Hocking  and
P. Doyle
J. Hocking
Affiliation:
Department of Mathematics Michigan State UniversityWells HallEast Lansing, Michigan 48824, U.S.A.
P. Doyle
Affiliation:
Department of Mathematics Michigan State UniversityWells HallEast 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 results here concern bijective continous functions from one connected separable n-manifold M to another N. If M has the property that every such function is necessarily a homeomorphism, then M is said to be strongly reversible. Strongly reversible manifolds having only compact boundary components are completely charaterized.

MSC classification

Secondary: 57N15: Topology of $E^n$, $n$-manifolds ($4 less n less infty$)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 2 , April 1983 , pp. 172 - 176
Copyright
Copyright © Australian Mathematical Society 1983

References

Dold, A. (1972) Lectures in algebraic topology (Springer Verlag).CrossRefGoogle Scholar
Doyle, P. H. and Hocking, J. G. (1976), ‘Continuous bijections on manifolds’, J. Austral. Math. Soc. 22. 257–263.CrossRefGoogle Scholar
Eichorn, J. (1978), ‘Die Kompaktifizierung offener Mannigfaltigkeiten zu geschlossenen I’, Math. Nachr. 85, 5–30.CrossRefGoogle Scholar
Kuratowski, K. (1968), Topology, Vol. 2 (Academic Press).Google Scholar
Pettey, D. H. (1970), ‘One-to-one mappings into a plane’, Fund. Math. 67, 209–218.CrossRefGoogle Scholar
Rajagopalan, M. and Wilansky, A. (1966), ‘Reversible topological spaces’, J. Austral. Math. Soc. 6, 129–138.CrossRefGoogle Scholar