Original scientific paper

https://doi.org/10.3336/gm.42.2.14

The spans of five star-like simple closed curves

Thelma West ; Department of Mathematics, University of Louisiana at Lafayette, LA 70504-1010, USA

Abstract

Let X be a continuum, that is a compact, connected, nonempty metric space. The span of X is the least upper bound of the set of real numbers r which satisfy the following conditions: there exists a continuum, C, contained in X × X such that d(x,y) is larger than or equal to r for all (x,y) in C and p1(C) = p2(C), where p1, p2 are the usual projection maps. The following question has been asked. If X and Y are two simple closed curves in the plane and Y is contained in the bounded component of the plane minus X, then is the span of X larger than the span of Y? We define a set of simple closed curves, which we refer to as being five star-like. We answer this question in the affirmative when X is one of these simple closed curves. We calculate the spans of the simple closed curves in this collection and consider the spans of various geometric objects related to these simple closed curves.

Keywords

Span; simple closed curve

Hrčak ID:

17952

URI

https://hrcak.srce.hr/17952

Publication date:

11.12.2007.

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