| Abstract: | ABSTRACT In the general setting of a complete, well-powered category A, we define and study two universal closure operations: regularization and extremalization, by means of regular and extremal subobjects of A. respectively. A general theorem of characterization of epimorphisms in A is given. When A is an epireflective subcategory of TOP, such operations are shown to coincide with A-closure 11] and epiclosure 2]. respectively. In the topological contest, regularization and extremalization are studied in detail and compared with r-closure, defined in 13]. |
