Realcompactifications of frames

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.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

1993

Author dc:creator

• Marcus, Nizar

Advisor dc:contributor.advisor

• Gilmour, Christopher Robert Anderson

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/14380

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/14380