Unusual and bijectively related manifolds

John G. Hocking

doi:10.4995/agt.2003.2026

Authors

John G. Hocking Michigan State University

DOI:

https://doi.org/10.4995/agt.2003.2026

Keywords:

Continuous bijection, 2-manifold

Abstract

A manifold is “unusual” if it admits of a continuous self-bijection which is not a homeomorphism. The present paper is a survey of work published over yearsaugmented with recent examples and results.

Downloads

Download data is not yet available.

Author Biography

John G. Hocking, Michigan State University

Department of Mathematics

References

P.H. Doyle and J.G. Hocking, A decomposition theorem for n-dimensional manifolds, Proc. Amer. Math. Soc. 13 (1962), 469-471.

P.H. Doyle and J.G. Hocking, Continuous bijections on manifolds, J. Austral. Math. Soc. 22 (1976), 257-263. http://dx.doi.org/10.1017/S1446788700014713

P.H. Doyle and J.G. Hocking, Strongly reversible manifolds, J. Austral. Math. Soc. Series A (1983), 172-176.

P.H. Doyle and J.G. Hocking, Bijectively related spaces I: Manifolds, Pac. J. Math. 3 No.1 (1984), 23-31. http://dx.doi.org/10.2140/pjm.1984.111.23

J. Eichorn, Die Kompactifizierung o ener mannigfaltigjeiten zu geschossenen I, Math. Nachr. 85 (1978), 5-30. http://dx.doi.org/10.1002/mana.19780850102

K. Kuratowski, Topology Vol 2, Academic Press, (1968).

D.H. Petty, One-to-one mappings into the plane, Fund. Math. 67 (1970), 209-218.

M. Rajagopalan and A. Wilansky, Reversible topological spaces, J. Austral. Math. Soc. 6 (1966), 129-138. http://dx.doi.org/10.1017/S1446788700004705

K. Whyburn, A non-topological 1 - 1 mapping onto E3, Bull. Amer. Math. Soc. 71 (1965), 523-537. http://dx.doi.org/10.1090/S0002-9904-1965-11313-1