C-connected frame congruences | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 7، دوره 6، Speical Issue on the Occasion of Banaschewski's 90th Birthday (I)، فروردین 2017، صفحه 51-66 اصل مقاله (465.42 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Dharmanand Baboolal1؛ Paranjothi Pillay1؛ Ales Pultr2 | ||
| 1School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban 4000, South Africa. | ||
| 2Department of Applied Mathematics and CE-ITI, MFF, Charles University, Malostransk\'e n\'am. 24, 11800 Praha 1, Czech Republic. | ||
| 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 | ||
| مراجع | ||
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