Fixed point sets of 1-dimensional Peano continua

John Rowlay Martin and Edward D. Tymchatyn

Vol. 89 (1980), No. 1, 147–149

DOI: 10.2140/pjm.1980.89.147

Abstract

It is shown that every nonempty closed subset of a 1-dimensional Peano continuum X is the fixed point set of some continuous self-mapping of X.

Mathematical Subject Classification 2000

Primary: 54H25

Secondary: 54F20

Milestones

Received: 23 February 1979

Revised: 5 July 1979

Published: 1 July 1980