The prime dicompletion of a di-uniformity on a plain texture

作者：Ozcag Selma^*; Brown Lawrence M

来源：Topology and Its Applications, 2011, 158(13): 1584-1594.

DOI：10.1016/j.topol.2011.05.028

• Plain texture
• Di-uniformity
• Maximal regular difilter
• Prime filter
• Prime Cauchy filter
• Completeness
• Prime dicompletion
• Separation
• Reflector
• Complementation

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.

• 出版日期2011-8-15