Vol. 37, No. 1, 1971

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Quasi-compactness and decompositions for arbitrary relations

Stanley Joseph Wertheimer

Vol. 37 (1971), No. 1, 253–263

If T is a relation, X the set of first elements and Y a set containing all the second elements, T(x) = {y Y |(x,y) T} and T1(y) = {x X|(x,y) T}. If T(x) T(y) is nonempty implies that T(x) = T(y), the relation T is semi-single-valued (ssv). Every ssv surjection defines a decomposition of X into point inverses and a decomposition of Y into point images. G. T. Whyburn has analyzed the ssv surjection T on X to Y in terms of these decomposition spaces and the natural mappings onto these spaces. He discusses quasi-compactness for ssv relations. It is the purpose of this paper to extend Whyburn’s analysis to include all relations.

Mathematical Subject Classification 2000
Primary: 54D30
Received: 2 June 1970
Published: 1 April 1971
Stanley Joseph Wertheimer