Cartesianclosed coreflective subcategories of uniform spaces
Authors:
M. D. Rice and G. J. Tashjian
Journal:
Trans. Amer. Math. Soc. 276 (1983), 289300
MSC:
Primary 54E15; Secondary 18B30, 18D15, 54B30
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 cartesianclosed. Specifically, we show that is cartesianclosed 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 cartesianclosed coreflective subcategories of Tychonoff spaces found in [10].
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198306845096
PII:
S 00029947(1983)06845096
Article copyright:
© Copyright 1983
American Mathematical Society
