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Abstract. Values of the compact interval and other spaces under coreflectors in the category of uniform spaces are studied. It is shown that any coreflector which changes the usual uniformity of the interval produces a new uniformity which contains all finite Baire partitions of the interval.

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Abstract. This paper characterizes the coreflective subcategories G of uniform spaces for which a natural function space structure generates the exponential law XY%Z = (XY)Z on G. Such categories are cartesian-closed. Specifically, we show that G is cartesian-closed in this way if and only if G 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].