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Exponential Objects in Coreflective or Quotient Reflective Subconstructs: A Comparison

In: Papers in Honour of Bernhard Banaschewski

Author

Listed:
  • E. Lowen-Colebunders

    (Vrije Universiteit Brussel, Departement Wiskunde)

  • C. Verbeeck

    (University of Antwerp, U.I.A., Departement Wiskunde-Informatica)

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.

Suggested Citation

  • E. Lowen-Colebunders & C. Verbeeck, 2000. "Exponential Objects in Coreflective or Quotient Reflective Subconstructs: A Comparison," Springer Books, in: Guillaume Brümmer & Christopher Gilmour (ed.), Papers in Honour of Bernhard Banaschewski, pages 247-256, Springer.
    • Handle: RePEc:spr:sprchp:978-94-017-2529-3_13
    DOI: 10.1007/978-94-017-2529-3_13
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