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.
@article{urn:eudml:doc:41697,
title = {On universal composition of maps.},
journal = {Publicacions Matem\`atiques},
volume = {35},
year = {1991},
pages = {363-374},
mrnumber = {MR1201562},
zbl = {0764.54006},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41697}
}
Cerin, Zvonko. On universal composition of maps.. Publicacions Matemàtiques, Tome 35 (1991) pp. 363-374. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41697/