On the Largest Coreflective Cartesian Closed Subconstruct of Prtop

E. Lowen-Colebunders and G. Sonck
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E. Lowen-Colebunders: Vrije Universiteit Brussel, Departement Wiskunde
G. Sonck: Vrije Universiteit Brussel, Departement Wiskunde

A chapter in Categorical Topology, 1996, pp 69-79 from Springer

Abstract: Abstract We show that the subconstruct Fing of Prtop, consisting of all finitely generated pre-topological spaces, is the largest Cartesian closed coreflective subconstruct of Prtop. This implies that in any coreflective subconstruct of Prtop, exponential objects are finitely generated. Moreover, in any finitely productive, coreflective subconstruct, exponential objects are precisely those objects of the subconstruct that are finitely generated. We give a counterexample showing that without finite productivity the previous result does not hold.

Keywords: pretopological space; finitely generated space; exponential object; quasi-variety; Cartesian closedness; 54B30; 18D15; 54A05 (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0263-3_6

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DOI: 10.1007/978-94-009-0263-3_6

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