Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exploring Core Regular Double Stone Algebras, CRDSA, II. Moving Towards
  Duality   This is the second in a series of three notes on an investigation into core
regular double Stone algebras, CRDSA, which are meant to be read in order. This
note begins our investigation of duality for CRDSA through bi-topological
spaces. More succinctly, duality through refinement of a pre- established
duality of pairwise Stone spaces and bounded distributive lattices. In this
note we establish necessary and sufficient conditions on a pairwise
zero-dimensional space such that it will have a core regular double Stone
algebra base. We note that these conditions can easily be relaxed to that which
is necessary for a pairwise zero-dimensional space to have a base that is not
as rigid as a CRDSA such as bounded distributive-pseudo complemented lattices
for example. Furthermore, these conditions give a topological representation
indicative of just how "nearly Boolean" CRDSA are, the closure of
non-clopen/complemented base elements are clopen/complemented base elements.
For the purposes of this note only we will call any pairwise zero-dimensional
space with a core regular double Stone algebra base a core regular double
pairwise zero-dimensional space. From that result we gain confidence to claim
that the category of core regular double Stone algebras is dually equivalent to
what we refer to in this note as the category of core regular double pairwise
Stone spaces. We validate this claim in the next note, Exploring Core Regular
Double Stone Algebras, CRDSA, III. Establishing Duality.

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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat