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d-Boolean algebras and their bitopological representation (2505.17806v1)
Published 23 May 2025 in math.GN
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 Stone bitopological spaces, which are compact and zero-dimensional bitopological spaces satisfying the T0 separation axiom.