Resumen de On universal composition of maps

Zvonko Cerin

• In this paper we shall introduce notions of F-universality and F-e-universality for maps between compact Hausdorff spaces and explore the behaviour of these properties under the operation of composition of maps. We consider both the quest for conditions on maps f and g which would imply that their composition g o f is either F-universal or F-e-universal and the quest for consequences on f and g when the composition g o f is either F-universal or F-e-universal. In our approach F is an arbitrary class of maps. For a special choice of F, the notion of F-universality reduces to Holsztysnki's notion of universality while F-e-universality reduces to Sanjurjo's notion of proximate universality.