ON EPIDENSE SUBCATEGORIES OF TOPOLOGICAL CATEGORIES

Dense subcategories were introduced by S. Marde?i? for an inverse system approach to (categorical) shape theory.

In this paper some internal characterizations of (epi,bi)dense subcategories of a topological category are given. We also show that if K ? A is a bidense subcategory then the “best approximation” of an A-object X by a K-inverse system is obtained by “modifications” of the structure of X.