Located sets on the line
Mark Mandelker · Pacific Journal of Mathematics · 1981
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.