The prime dicompletion of a di-uniformity on a plain texture |
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Authors: | Selma Ö zç a?,Lawrence M. Brown |
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Affiliation: | Hacettepe University, Faculty of Science, Department of Mathematics, 06532 Beytepe, Ankara, Turkey |
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Abstract: | Working within a plain texture (S,S), the authors construct a completion of a dicovering uniformity υ on (S,S) in terms of prime S-filters. In case υ is separated, a separated completion is then obtained using the T0-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,ρ) is presented. |
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Keywords: | primary, 54E15, 54A05 secondary, 06D10, 03E20, 54A40, 54D10, 54D15, 54E35 |
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