Vol. 95, No. 2, 1981

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Located sets on the line

Mark Mandelker

Vol. 95 (1981), No. 2, 401–409

Located sets are sets from which the distance of any point may be measured; they are used extensively in modern constructive analysis. Here a general method is given for the construction of all located sets on the line. It is based on a characterization of a located set in terms of the resolution of its metric complement into a union of disjoint open intervals. The characterization depends on a strong countability condition for the intervals, called the locating condition. Included as a special case is the characterization and construction of compact sets. The techniques used are in accord with the principles of Bishop’s Foundations of Constructive Analysis, 1967.

Mathematical Subject Classification 2000
Primary: 03F65
Secondary: 26A03
Received: 4 May 1979
Revised: 9 June 1980
Published: 1 August 1981
Mark Mandelker