Bijectively related spaces. I. Manifolds

P. H. Doyle, III and John Gilbert Hocking

Vol. 111 (1984), No. 1, 23–33

DOI: 10.2140/pjm.1984.111.23

Abstract

The following equivalence relation is introduced: Two (Hausdorff) spaces X and Y are bijectvely related if there exist continuous bijections f : X → Y and g : X → Y . This first paper considers the case in which X and Y are connected manifolds. If either f or g is not a homeomorphism, then each space is necessarily non-reversible and hence this study produces more knowledge of such spaces. The chief results here are the existence theorem (Theorem 2) and, perhaps, Corollary 12, which states that a simply-connected manifold having only compact boundary components is reversible.

Mathematical Subject Classification 2000

Primary: 57N99

Secondary: 54C99

Milestones

Received: 21 April 1981

Revised: 4 April 1983

Published: 1 March 1984