C-connected frame congruences

نویسندگان
Baboolal, Dharmanand ID 1
Pillay, Paranjothi ID 2
Pultr, Ales ID 3

1 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa.

2 School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa.

3 Department of Applied Mathematics and CE-ITI, MFF, Charles University, Malostransk\'e n\'am. 24, 11800 Praha 1, Czech Republic.

doi
چکیده

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.

کلیدواژه‌ها
frame, frame congruence, congruence and sublocale lattice, connectedness, $T_D$-spatiality