Displaying similar documents to “Fan-Gottesman type compactification of frames”

Pseudocompactness and the cozero part of a frame

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 σ -frame and to Alexandroff spaces.

Realcompactification of frames

Nizar Marcus (1995)

Commentationes Mathematicae Universitatis Carolinae

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We give a construction of Wallman-type realcompactifications of a frame L by considering regular sub σ -frames the join of which generates L . In particular, we show that the largest such regular sub σ -frame gives rise to the universal realcompactification of L .

Samuel compactification and uniform coreflection of nearness σ -frames

Inderasan Naidoo (2006)

Czechoslovak Mathematical Journal

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We introduce the structure of a nearness on a σ -frame and construct the coreflection of the category 𝐍 σ F r m of nearness σ -frames to the category 𝐊 R e g σ F r m of compact regular σ -frames. This description of the Samuel compactification of a nearness σ -frame is in analogy to the construction by Baboolal and Ori for nearness frames in [1] and that of Walters for uniform σ -frames in [11]. We also construct the uniform coreflection of a nearness σ -frame, that is, the coreflection of the category of 𝐍 σ F r m to...