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Let X be a completely regular locale. We present a construction which shows that every locale f : Y → X over X has a completely regular proper reflection in the slice category Loc/X and the reflection map is a dense embedding if and only if Y is completely regular. Let X be a locale. We know that the category Loc(Sh(X)) of internal locales in the sheaves topos Sh(X) is equivalent to the slice category Loc/X of locales over X (see [1], [2]). Also a localic map f : Y → X is proper if and only if it corresponds to a compact internal locale in the topos Sh(X) (see [8]). By a classical result given by B. Banaschewski and C. J. Mulvey in [3], we know that the category of compact completely regular locales (compact regular locales) is reflective in the category of locales. So the following question is interesting: Dose there exist a compact completely regular reflection for every internal locale in Sh(X)? Suppose f : Y → X is a locale over X. Let g : Z → X be a proper map with Z completely regular. We call g : Z → X a completely regular proper reflection of f : Y → X if there exists a localic map h : Y → Z such that f = gh,

Completely regular proper reflection of locales over a given locale