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Quasi-compactness and decompositions for arbitrary relations

1971
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Pacific Journal of Mathematics
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If T is a relation, X the set of first elements and Y a set containing all the second elements, T(x) = {yeY\(x f y)e T] and T~\y) = {x e X | (a?, y) e T}. If T(x) n 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

doi:10.2140/pjm.1971.37.253
fatcat:skzz7hr7orbsjdwb7l2qkbhmca