The Prime Dicompletion Of A Di-Uniformity On A Plain Texture

Abstract

Working within a plain texture (S, S), the authors construct a completion of a dicovering uniformity v on (S, S) in terms of prime S-filters. In case v is separated, a separated completion is then obtained using the To-quotient, and it is shown that this construction produces a reflector. For a totally bounded di-uniformity it is verified that these constructions lead to dicompactifications of the uniform ditopology. A condition is given under which complementation is preserved on passing to these completions, and an example on the real texture (R, R, rho) is presented. (C) 2011 Elsevier B.V. All rights reserved.