Exponential Objects in Coreflective or Quotient Reflective Subconstructs: A Comparison

E. Lowen-Colebunders () and C. Verbeeck ()
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E. Lowen-Colebunders: Vrije Universiteit Brussel, Departement Wiskunde
C. Verbeeck: University of Antwerp, U.I.A., Departement Wiskunde-Informatica

A chapter in Papers in Honour of Bernhard Banaschewski, 2000, pp 247-256 from Springer

Abstract: 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.

Keywords: exponential object; pre-approach space; pretopological space; coreflective subconstruct; quotient reflective subconstruct.; 18B99; 18D15; 54A05; 54B30; 54C35; 54E35 (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-017-2529-3_13

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DOI: 10.1007/978-94-017-2529-3_13

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