Semigroups with identity on Peano continua

William W. Williams

Vol. 69 (1977), No. 2, 557–569

DOI: 10.2140/pjm.1977.69.557

Abstract

A continuum is cell-cyclic if every cyclic element is a finite dimensional cell. We show that any finite dimensional cell-cyclic Peano continuum X admits a commutative semigroup with zero and identity, and apply this to show that if X is also homogeneous it is a point.

Mathematical Subject Classification 2000

Primary: 54F20, 54F20

Secondary: 22A15

Milestones

Received: 3 November 1975

Published: 1 April 1977