Abstract
We give an internal characterization of the exponential objects in the constructPrtop and investigate Cartesian closedness for coreflective or topological full subconstructs ofPrtop. If $ is the set {0} ∪ {1/n;n ≥ 1} endowed with the topology induced by the real line, we show that there is no full coreflective subconstruct ofPrtop containing $ and which is Cartesian closed. With regard to topological full subconstructs ofPrtop we give an example of a Cartesian closed one that is large enough to contain all topological Fréchet spaces and allT 1 pretopological Fréchet spaces.
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Lowen-Colebunders, E., Sonck, G. Exponential objects and Cartesian closedness in the constructPrtop . Appl Categor Struct 1, 345–360 (1993). https://doi.org/10.1007/BF00872940
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DOI: https://doi.org/10.1007/BF00872940