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A hereditary class on a set X is a nonempty collection of subsets closed under heredity. The aim of this paper is to introduce and study strong forms of u-compactness in generalized topological spaces with respect to a hereditary class, called  SuH-compactness and S- SuH-compactness. Also several of their properties are presented. Finally some eects of various kinds of functions on them are studied.

New forms of -compactness with respect to hereditary classes