V. F. Laguna

INTERNAL FUNDAMENTAL SEQUENCES AND APPROXIMATIVE RETRACTS

Abstract We introduce the notion of internal fundamental sequence and prove that any shape morphism from an arbitrary compactum X to an internally movable compactum Y is induced by an internal fundamental sequence. We use this special kind of fundamental sequences to give characterizations and some properties of AANR C -sets and AANR N -sets. The paper ends with a section devoted to internal FANRs.

Generalized refinable maps and images of FANR's

In this paper we study certain shape and homotopy properties of refinable and weakly refinable maps. In particular we give a sufficient condition for a weakly refinable map to be a homotopy domination when the codomain is an ANR. We also characterise those weakly refinable maps which preserve FANRs and using a result of Boxer we characterise the weakly refinable maps which preserve ANRs.