Displaying similar documents to “On extended frames”

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...

Weil uniformities for frames

Jorge Picado (1995)

Commentationes Mathematicae Universitatis Carolinae

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In pointfree topology, the notion of uniformity in the form of a system of covers was introduced by J. Isbell in [11], and later developed by A. Pultr in [14] and [15]. Another equivalent notion of locale uniformity was given by P. Fletcher and W. Hunsaker in [6], which they called “entourage uniformity”. The purpose of this paper is to formulate and investigate an alternative definition of entourage uniformity which is more likely to the Weil pointed entourage uniformity, since it is...