<p>S4-subordination algebras are a generalization of the closure algebras. In this paper, we give a topological representation for S4-subordination algebras by means of bitopological spaces <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\langle X,\tau ,\tau _{S}\rangle $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">⟨</mo> <mi>X</mi> <mo>,</mo> <mi>τ</mi> <mo>,</mo> <msub> <mi>τ</mi> <mi>S</mi> </msub> <mo stretchy="false">⟩</mo> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\langle X,\tau \rangle $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">⟨</mo> <mi>X</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">⟩</mo> </mrow> </math></EquationSource> </InlineEquation> is a Stone space and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\tau _{S}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mi>S</mi> </msub> </math></EquationSource> </InlineEquation> is a topology that enables the characterization of the subordination relation. We apply this bitopological representation to give a characterization of S5-subordination algebras and lattice subordinations. We also show that there exists a bijective correspondence between congruence compatible with the subordination and certain closed subsets of the Stone space <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\langle X,\tau \rangle $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">⟨</mo> <mi>X</mi> <mo>,</mo> <mi>τ</mi> <mo stretchy="false">⟩</mo> </mrow> </math></EquationSource> </InlineEquation> that are also saturated sets of the space <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\langle X,\tau _{S}\rangle $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">⟨</mo> <mi>X</mi> <mo>,</mo> <msub> <mi>τ</mi> <mi>S</mi> </msub> <mo stretchy="false">⟩</mo> </mrow> </math></EquationSource> </InlineEquation>. Additionally, we explore two types of morphisms between S4-subordination algebras: one based on Boolean homomorphisms and another based on meet-homomorphisms. Finally, we provide a topological representation for each type of morphism.</p>

A Bitopological Duality for Some Subordination Boolean Algebras

期刊论文
发表日期：

2026年7月23日

查看全文

Sergio A. Celani

摘要

S4-subordination algebras are a generalization of the closure algebras. In this paper, we give a topological representation for S4-subordination algebras by means of bitopological spaces $\langle X,\tau ,\tau _{S}\rangle $ $⟨ X, τ, τ_{S} ⟩$ , where $\langle X,\tau \rangle $ $⟨ X, τ ⟩$ is a Stone space and $\tau _{S}$ $τ_{S}$ is a topology that enables the characterization of the subordination relation. We apply this bitopological representation to give a characterization of S5-subordination algebras and lattice subordinations. We also show that there exists a bijective correspondence between congruence compatible with the subordination and certain closed subsets of the Stone space $\langle X,\tau \rangle $ $⟨ X, τ ⟩$ that are also saturated sets of the space $\langle X,\tau _{S}\rangle $ $⟨ X, τ_{S} ⟩$ . Additionally, we explore two types of morphisms between S4-subordination algebras: one based on Boolean homomorphisms and another based on meet-homomorphisms. Finally, we provide a topological representation for each type of morphism.