Unusual and bijectively related manifolds

John G. Hocking

United States

Michigan State University

Department of Mathematics

Submitted: 2013-12-16

|

Accepted: 2013-12-16

|

Published: 2003-10-01

DOI: https://doi.org/10.4995/agt.2003.2026
Funding Data

Downloads

Keywords:

Continuous bijection, 2-manifold

Supporting agencies:

This research was not funded

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.

Show more Show less

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

Show more Show less