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.
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Dedicated to Professor Bernhard Banaschewski on the occasion of his 70th birthday
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© 2000 Springer Science+Business Media Dordrecht
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Lowen-Colebunders, E., Verbeeck, C. (2000). Exponential Objects in Coreflective or Quotient Reflective Subconstructs: A Comparison. In: Brümmer, G., Gilmour, C. (eds) Papers in Honour of Bernhard Banaschewski. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2529-3_13
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DOI: https://doi.org/10.1007/978-94-017-2529-3_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5540-8
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