(1) Departement Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium e-mail;(2) Departement Wiskunde-Informatica, University of Antwerp, U.I.A., Universiteitsplein 1, 2610 Wilrijk, Belgium, e-mail
Abstract:
We prove that in the construct PRAP of pre-approach spaces the class of exponential objects completely determines the exponential objects in certain subconstructs. We show that Exp B Exp PRAP for every coreflective subconstruct B and from this inclusion we deduce the equality Exp B = B Exp PRAP for every subconstruct B that is coreflective and finitely productive. We prove that the same equality holds for non-trivial quotient reflective subconstructs. These results induce well known answers to similar questions on the construct of pretopological spaces and are compared to the topological situation.