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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On the spans and width of simple triods


Author: Thelma West
Journal: Proc. Amer. Math. Soc. 105 (1989), 776-786
MSC: Primary 54F20; Secondary 54F25, 54F50
DOI: https://doi.org/10.1090/S0002-9939-1989-0953014-2
MathSciNet review: 953014
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Abstract: In 1964 the concept of the span of a metric space was introduced by A. Lelek. Since that time, some modified versions of the span have been considered. To date, the metric spaces for which the various spans have been explictly calculated have mainly been objects for which the span is zero. In this paper, we calculate and estimate the spans of simple triods.

Questions have been raised concerning the relationships between these various versions of spans. For instance, it was conjectured that the surjective span is always at least a half of the span. We find that these spans are equal for some types of simple triods. Another problem concerning simple triods asks if the surjective semispan and the surjective span of them are always equal. This problem is solved positively for some classes of simple triods.

In 1961 the width of a treelike continuum was introduced by C. E. Burgess. The relationship of the width and the span is only vaguely known. We involve the widths of simple triods in our estimations of the span.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0953014-2
Article copyright: © Copyright 1989 American Mathematical Society