Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58536Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)20170101C-connected frame congruences516634405ENDharmanand BaboolalSchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa.0000-0001-6737-1656Paranjothi PillaySchool of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa.Ales PultrDepartment of Applied Mathematics and CE-ITI, MFF, Charles University, Malostransk\'e n\'am. 24, 11800 Praha 1, Czech Republic.Journal Article20160601We 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.https://cgasa.sbu.ac.ir/article_34405_5a2102b74343052718d395077541ad72.pdf