Abstract
Some of the relationships among the topological notions: ‘Hausdorff’, ‘compact’, ‘perfect’, and ‘closed’ are abstracted to a more general categorical setting, where they are shown to remain intact. An investigation is made of factorization structures (especially for single morphisms) and their relationships to strong limit operators and to the Pumplu¨n-Ro¨hrl Galois correspondence between classes of objects and classes of morphisms in any category. Many examples as well as internal characterizations of Galois-closed classes are provided.
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