Realcompactifications of frames
Master Thesis
1993
Permanent link to this Item
Authors
Supervisors
Journal Title
Link to Journal
Journal ISSN
Volume Title
Publisher
Publisher
University of Cape Town
Faculty
License
Series
Abstract
The first notion of realcompactness in frames was introduced by Reynolds [1979], and it was shown by Madden and Vermeer [1986] that this coincides with the Lindelof property. My thesis advisor suggested that more general realcompactifications of a frame L could be constructed by considering regular sub σ-frames which join generate L. This was motivated by the fact that the Alexandroff bases, which are used to construct the Wallman realcompactifications of a space X, are, as shown by Gilmour, simply the regular sub σ-frames of the frame of open sets of X. The key definition of realcompactness needed here is due to Schlitt [1990] and it is his construction of the universal realcompactification that we modify in order to obtain the Wallman realcompactifications.
Description
Bibliography: leaves 53-57.
Reference:
Marcus, N. 1993. Realcompactifications of frames. University of Cape Town.