The pullback closure operator and generalisations of perfectness
The author studies a closure operator \(\Phi_{(R,r)}\) [in the sense of \textit{E. Giuli} and \textit{D. Dikranyan}, Topology Appl. 27, 129-143 (1987; Zbl 0634.54008)] associated with a pointed endofunctor \((R,r)\), defined by means of pullback. In the case of a reflector of a topological category this was done by \textit{D. Dikranyan} [Suppl. Rend. Circ. Mat. Palermo, II. Ser. 29, 105-160 (1992; Zbl 0782.54009)]. The author offers the first systematic study of this closure operator in full generality and studies various notions of perfectness relative to the pointed endofunctor \({(R,r)}\) and its pullback closure operator \(\Phi_{(R,r)}\).
scientific article; zbMATH DE number 1053694