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On Homogeneous Images of Compact Ordered Spaces

Published online by Cambridge University Press:  20 November 2018

J. Nikiel  and
E.D. Tymchatyn
J. Nikiel
Affiliation:
Department of Mathematics, University of Saskatchewan, Saskatoon Saskatchewan, S7N 0W0
E.D. Tymchatyn
Affiliation:
Department of Mathematics, University of Saskatchewan, Saskatoon Saskatchewan, S7N 0W0
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Abstract

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We answer a 1975 question of G R Gordh by showing that if X is a homogeneous compactum which is the continuous image of a compact ordered space then at least one of the following holds

(I) X is metrizable, (II) dim X = 0 or (III) X is a union of finitely many pairwise disjoint generalized simple closed curves.

We begin to examine the structure of homogeneous 0-dimensional spaces which are continuous images of ordered compacta.

Keywords

54F0554C05arccompact ordered spacecontinuous imagehomogeneousstrongly homogeneousdendron
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 2 , 01 April 1993 , pp. 380 - 393
Copyright
Copyright © Canadian Mathematical Society 1993

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