Vol. 30, No. 3, 1969

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On universal tree-like continua

Jack Wyndall Rogers Jr.

Vol. 30 (1969), No. 3, 771–775
Abstract

R. M. Schori has conjectured that if T is a tree, but not an arc, then there is no universal T-like continuum. We show that if G is a finite collection of trees and there is a universal G-like continuum, then each element of G is an arc. It then follows that if G is a finite collection of one-dimensional (connected) polyhedra, and there is a universal G-like continuum, then each element of G is an arc.

Mathematical Subject Classification
Primary: 54.55
Milestones
Received: 18 November 1968
Published: 1 September 1969
Authors
Jack Wyndall Rogers Jr.