Semiregular frames
Jan Paseka, Bohumil Šmarda (1990)
Archivum Mathematicum
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Jan Paseka, Bohumil Šmarda (1990)
Archivum Mathematicum
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Bernhard Banaschewski, Christopher Gilmour (1996)
Commentationes Mathematicae Universitatis Carolinae
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A characterization of the cozero elements of a frame, without reference to the reals, is given and is used to obtain a characterization of pseudocompactness also independent of the reals. Applications are made to the congruence frame of a -frame and to Alexandroff spaces.
Nizar Marcus (1995)
Commentationes Mathematicae Universitatis Carolinae
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We give a construction of Wallman-type realcompactifications of a frame by considering regular sub -frames the join of which generates . In particular, we show that the largest such regular sub -frame gives rise to the universal realcompactification of .
Inderasan Naidoo (2006)
Czechoslovak Mathematical Journal
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We introduce the structure of a nearness on a -frame and construct the coreflection of the category of nearness -frames to the category of compact regular -frames. This description of the Samuel compactification of a nearness -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform -frames in [11]. We also construct the uniform coreflection of a nearness -frame, that is, the coreflection of the category of to...