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In "Centre of Core Regular Double Stone Algebra" (CRDSA), many useful resultsare shown that begin to indicate the nearly Boolean nature of CRDSA which wefocus on here. We define the node set lattice through the well known binaryoperations of ternary set partitions and show the resultant lattice isisomorphic to C3^J where C3 is the 3 element chain CRDSA. We derive that everyCRDSA is a subdirect product of C3 similarly as for Boolean algebras and C2. Weuse these results to show that every Boolean algebra is the center of someCRDSA. Next we show that C3 is primal implying that the variety generated by itis dually equivalent to the category of Boolean algebras. In some sense this isa last step towards our goal of establishing CRDSA as nearly Boolean, butleaves us a bit dissatisfied. Hence we continue by establishing a dualitybetween the category of CRDSA and specifically crafted bi-topological spaces.Towards this end we first establish necessary and sufficient conditions on apairwise zero-dimensional space such that it will have a CRDSA base B1. We notethat these conditions are indicative of how nearly Boolean CRDSA are. Forexample, if u in B1 is not clopen/complemented then Cl(u) is in B1 and isclopen/complemented. Then we establish necessary and sufficient conditions fora bi-continuous map to have an inverse that is a CRDSA homomorphism againindicating how nearly Boolean CRDSA are, these inverses must respect theappropriate conditions on the boundary of non-clopen elements of B1. Inculmination we show the category of core regular double Stone algebras isdually equivalent to the category of what we call core regular double pairwiseStone spaces. We note that the conditions for this duality can easily berelaxed to yield a duality for a less rigid class lattices than CRDSA, boundeddistributive pseudo-complemented lattices for example.

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