论文信息 - On Homogeneous Images of Compact Ordered Spaces

On Homogeneous Images of Compact Ordered Spaces

Abstract 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.

J. Nikiel | E. Tymchatyn

[1] J. Nikiel. Orderability properties of a zero-dimensional space which is a continuous image of an ordered compactum , 1989 .

[2] K. P. Hart,et al. A method for constructing ordered continua , 1985 .

[3] J. Mill,et al. Subbase characterizations of subspaces of compact trees , 1982 .

[4] L. Treybig. Separation by finite sets in connected, continuous images of ordered compacta , 1979 .

[5] G T Whyburn,et al. Cut points in general topological spaces. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[6] S. Mardešić. Images of ordered compacta are locally peripherally metric , 1967 .

[7] L. Treybig. Concerning homogeneity in totally ordered, connected topological space. , 1963 .

[8] L. Oversteegen,et al. On hereditarily decomposable hereditarily equivalent non-metric continua , 1990 .

[9] J. Nikiel. Images of arcs - a nonseparable version of the Hahn-Mazurkiewicz theorem , 1988 .

[10] J. Mill. Characterization of some zero-dimensional separable metric spaces , 1981 .

[11] Harold Bennett,et al. Topology and order structures , 1981 .

[12] J. J. Charatonik. Open Mappings of Universal Dendrites , 1980 .

[13] G. Gordh. On homogeneous hereditarily unicoherent continua , 1975 .

[14] Keith Devlin,et al. The Souslin problem , 1974 .

[15] M. A. Maurice,et al. Compact ordered spaces , 1964 .