A continuous partial order for Peano continua

Virginia E. Walsh Knight

Vol. 30 (1969), No. 1, 141–153

DOI: 10.2140/pjm.1969.30.141

Abstract

A theorem of R. J. Koch states that a compact continuously partially ordered space with some natural conditions on the partial order is arcwise connected. L. E. Ward, Jr., has conjectured that Koch’s arc theorem implies the well-known theorem of R. L. Moore that a Peano continuum is arcwise connected. In this paper Ward’s conjecture is proved.

Mathematical Subject Classification

Primary: 54.55

Milestones

Received: 9 December 1968

Published: 1 July 1969