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The Nearly Boolean Nature of Core Regular Double Sone Algebras, CRDSA (Ternary Set Partitions, CRDSA, Embeddings and Dual Equivalences) by Clouse, Daniel J. is a scholarly article available to read on EtoBox.

What is The Nearly Boolean Nature of Core Regular Double Sone Algebras, CRDSA (Ternary Set Partitions, CRDSA, Embeddings and Dual Equivalences) about?

In "Centre of Core Regular Double Stone Algebra" (CRDSA), many useful results are shown that begin to indicate the nearly Boolean nature of CRDSA which we focus on here. We define the node set lattice through the well known binary operations of ternary set partitions and show the resultant lattice is isomorphic to C3^J where C3 is the 3 element chain CRDSA. We derive that every CRDSA is a subdirect product of C3 similarly as for Boolean algebras and C2. We use these results to show that every Boolean algebra is the center of some CRDSA. Next we show that C3 is primal implying that the variety generated by it is dually equivalent to the category of Boolean algebras. In some sense this is a last step towards our goal of establishing CRDSA as nearly Boolean, but leaves us a bit dissatisfied. Hence we continue by establishing a duality between the category of CRDSA and specifically crafted bi-topological spaces. Towards this end we first establish necessary and sufficient conditions on a pairwise zero-dimensional space such that it will have a CRDSA base B1. We note that these conditions are indicative of how nearly Boolean CRDSA are. For example, if u in B1 is not clopen/complemented

Author

Clouse, Daniel J.

Published

2018

Language

EN