  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 then Cl(u) is in B1 and is
clopen/complemented. Then we establish necessary and sufficient conditions for
a bi-continuous map to have an inverse that is a CRDSA homomorphism again
indicating how nearly Boolean CRDSA are, these inverses must respect the
appropriate conditions on the boundary of non-clopen elements of B1. In
culmination we show the category of core regular double Stone algebras is
dually equivalent to the category of what we call core regular double pairwise
Stone spaces. We note that the conditions for this duality can easily be
relaxed to yield a duality for a less rigid class lattices than CRDSA, bounded
distributive pseudo-complemented lattices for example.
