d-Boolean algebras and their bitopological representation

2025/05/23 by Yang, Hang, Zhang, Dexue · 1 citation
#06E75 #18F70 #54E55 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2505.17806

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.

Cited by

• d-Spectral Bitopological Spaces

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• Boolean sets, skew Boolean algebras and a non-commutative Stone duality
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• d-Spectral Bitopological Spaces
• The Stone's Representation Theorems and compactifications of a discrete space
• Duality Between Uniform Spaces and Boolean Algebras