Some homotopic properties of functors with bounded supports - Zarichny, M.M. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
It is proved that Shchepin-normal functors with finite supports in the category of compacta are continuous in the topology of homotopically n-regular Kuratowski convergence in the space of LC^n-subsets of a metric compactum. These functors also preserve the property of mappings of polyhedra to induce an isomorphism of homotopic groups of dimension not greater than n.