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

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...