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Minimal arcs in metric spaces
Published online by Cambridge University Press: 09 April 2009
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In this paper we discuss the existence of an are of minimal length joining two arbitrary, yet fixed points in a complete metric space, where the metric is restricted only by the properties (A) and (B) given below. It is shown that under these conditions an arc of least length joining any two fixed points exists, and is unique. In addition, its length is shown to be equal to the metrie distance between the points.
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- Copyright © Australian Mathematical Society 1975
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