%0 Journal Article
%T C-connected frame congruences
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Baboolal, Dharmanand
%A Pillay, Paranjothi
%A Pultr, Ales
%D 2017
%\ 01/01/2017
%V 6
%N Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)
%P 51-66
%! C-connected frame congruences
%K frame
%K frame congruence
%K congruence and sublocale lattice
%K connectedness
%K $T_D$-spatiality
%R
%X We discuss the congruences $\theta$ that are connected as elements of the (totally disconnected) congruence frame $\CF L$, and show that they are in a one-to-one correspondence with the completely prime elements of $L$, giving an explicit formula. Then we investigate those frames $L$ with enough connected congruences to cover the whole of $\CF L$. They are, among others, shown to be $T_D$-spatial; characteristics for some special cases (Boolean, linear, scattered and Noetherian) are presented.
%U https://cgasa.sbu.ac.ir/article_34405_5a2102b74343052718d395077541ad72.pdf