Completeness properties of function rings in pointfree topology

Bernhard Banaschewski; Sung Sa Hong

Displaying similar documents to “Completeness properties of function rings in pointfree topology”

Contracting the socle in rings of continuous functions

Themba Dube (2010)

Rendiconti del Seminario Matematico della Università di Padova

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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.

N-compact frames

Greg M. Schlitt (1991)

Commentationes Mathematicae Universitatis Carolinae

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We investigate notions of $ℕ$ -compactness for frames. We find that the analogues of equivalent conditions defining $ℕ$ -compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame ‘ $ℕ$ -cubes’ are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial $ℕ$ -compactness form a much larger class, and better embody what ‘ $ℕ$ -compact frames’ should be. This latter property is expressible...