Exponential Objects in Coreflective or Quotient Reflective Subconstructs: A Comparison

摘要

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 #beta# is contained in Exp PRAP for every coreflective subconstruct #beta# and from this inclusion we deduce the equality Exp #beta#=#beta# intersect Exp PRAP for every subconstruct #beta# 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.