The prime dicompletion of a di-uniformity on a plain texture
This paper deals with the problem of constructing a dicompletion for a di-uniformity \(\upsilon\) on a texture \((S,\mathcal{S})\). The problem appears to be hard and the authors confine their attention to plain textures (the ones for which the texturing is closed under arbitrary unions). They construct a completion of \(\upsilon\) in terms of prime \(\mathcal S\)-filters. When \(\upsilon\) is separated, a separated completion is obtained using the \(T_0\)-quotient, and it is proved that this construction produces a reflector making the category of separated complete di-uniform spaces a full reflective subcategory of the category of separated di-uniform spaces. Then it is noted, as expected, that for totally bounded di-uniformities these constructions lead to dicompactifications of the uniform ditopology.
scientific article; zbMATH DE number 5935903
scientific article