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On the Spans and Width of Simple Triods

Thelma West

1989
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Proceedings of the American Mathematical Society
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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
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... urjective 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. 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 (cf. [2, 3] ). To date the metric spaces for which the various spans have been explicitly calculated have mainly been objects for which the span is zero. It is still an unsettled problem whether or not continua of span zero are arclike. In this paper we calculate and estimate the spans of simple triods. Questions have been raised concerning the relationships between these various versions of span. For instance, it was conjectured that the surjective span is always at least a half of the span (see [3, p. 37]). We find that these spans are equal for some types of simple triods (see 2.4). Another problem concerning simple triods asks if the surjective semispan and the surjective span of them are always equal (see [3, p. 38]). This problem is solved positively in §2 for some classes of simple triods. In 1961 the width of a treelike continuum was introduced by C. E. Burgess (see [1, p. 447]). The relationship of the width and the span is only vaguely

doi:10.2307/2046932
fatcat:koxplooaznezpm5yvowpw2pavm