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In this paper the lattice of all epidense subcategories of a topological category is investigated by defining the Lα-objects for every cardinal number α. It is proved that the full subcategory Lα A of a topological category A whose objects are all Lα-objects is an extremal epidense subcategory of A. If A is universal, then the lattice of all epidense subcategories contained in LoA is isomorphic...
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