d-Boolean algebras and their bitopological representation
arXiv:2505.17806 · doi:10.1016/j.topol.2026.109740
Abstract
We present a Stone duality for bitopological spaces in analogy to the duality between Stone spaces and Boolean algebras, in the same vein as the duality between d-sober bitopological spaces and spatial d-frames established by Jung and Moshier. Precisely, we introduce the notion of d-Boolean algebras and prove that the category of such algebras is dually equivalent to the category of compact and zero-dimensional bitopological spaces satisfying the T0 separation axiom.
30 pages