Based on a rather arbitrary class of morphisms in a category, which play the role of ``closed maps'', we present a general approach to separation and compactness, both at the object and the morphism levels. It covers essential parts of the classical topological theory, generalizes various previous categorical treatments of the theme, and allows for a number of less expected applications outside topology.
Homology, Homotopy and Applications, Vol. 1, 1999, No. 6, pp 147-161
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