This is the first in a series of three notes on an investigation into core regular double Stone algebras, CRDSA, and are meant to be read in order. They were born out of a model of network security where individual nodes are considered to be in one of 3 states. Applications of these results are being explored, results of at least one of which will be published at a later date. The two notes following this will establish a duality between the category of CRDSA and specifically crafted bi-topological spaces. Let J be any non-empty set of network nodes, not necessarily finite. We denote the node set bounded distributive lattice through the pairwise disjoint subsets of J with the well known binary operations of ternary set partitions and note J = 1 is our minimal case. We then show the resultant bounded distributive lattice is isomorphic to direct products of the 3 element chain, C_3. We then derive that every CRDSA is a subdirect product of C_3. We use these results along with a few known 查看全文>>