Cartesian-closed coreflective subcategories of uniform spaces

Authors:
M. D. Rice and G. J. Tashjian

Journal:
Trans. Amer. Math. Soc. **276** (1983), 289-300

MSC:
Primary 54E15; Secondary 18B30, 18D15, 54B30

DOI:
https://doi.org/10.1090/S0002-9947-1983-0684509-6

MathSciNet review:
684509

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Abstract: This paper characterizes the coreflective subcategories of uniform spaces for which a natural function space structure generates the exponential law on . Such categories are cartesian-closed. Specifically, we show that is cartesian-closed in this way if and only if is inductively generated by a finitely productive family of locally fine spaces. The results divide naturally into two cases: those subcategories containing the unit interval are generated by precompact spaces, while the subcategories not containing the unit interval are generated by spaces which admit an infinite cardinal. These results may be used to derive the characterizations of cartesian-closed coreflective subcategories of Tychonoff spaces found in [**10**].

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0684509-6

Article copyright:
© Copyright 1983
American Mathematical Society