Characterising Points Which Make P-frames
Document Type
Article
Publication Date
12-22-2015
Abstract
A P -frame is a completely regular frame whose cozero part is a Boolean algebra. It is known that these frames are precisely those the points of whose Stone–Čech compactification are all of a certain kind, akin to P -points in Tychonoff spaces. Our principal aim is to characterise such points in all completely regular frames using filters in sublocale lattices. We thus define a filter on (as opposed to “in”) a locale L to be a filter in the lattice of S(L) of sublocales of L, so that its members are sublocales of L and not elements of L. We define convergence for these filters and use that to characterise the points alluded to above. As another application, we also define clustering for these filters and characterise compact locales in terms of both convergence and clustering.
Recommended Citation
T. Dube & O. Ighedo: Characterising points which make P-frames. Topology and its Applications, 200 (2016), 146 - 159. https://doi.org/10.1016/j.topol.2015.12.017
Peer Reviewed
1
Copyright
Elsevier
Comments
This article was originally published in Topology and its Applications, volume 200, in 2016. https://doi.org/10.1016/j.topol.2015.12.017