کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4595918 1336141 2015 34 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
De Vries powers: A generalization of Boolean powers for compact Hausdorff spaces
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
De Vries powers: A generalization of Boolean powers for compact Hausdorff spaces
چکیده انگلیسی

We generalize the Boolean power construction to the setting of compact Hausdorff spaces. This is done by replacing Boolean algebras with de Vries algebras (complete Boolean algebras enriched with proximity) and Stone duality with de Vries duality. For a compact Hausdorff space X and a totally ordered algebra A  , we introduce the concept of a finitely valued normal function f:X→Af:X→A. We show that the operations of A   lift to the set FN(X,A)FN(X,A) of all finitely valued normal functions, and that there is a canonical proximity relation ≺ on FN(X,A)FN(X,A). This gives rise to the de Vries power construction, which when restricted to Stone spaces, yields the Boolean power construction.We prove that de Vries powers of a totally ordered integral domain A are axiomatized as proximity Baer Specker A  -algebras; that is, the pairs (S,≺)(S,≺), where S is a torsion-free A-algebra generated by its idempotents which is a Baer ring, and ≺ is a proximity relation on S. We introduce the category of proximity Baer Specker A-algebras and proximity morphisms between them, and prove that this category is dually equivalent to the category of compact Hausdorff spaces and continuous maps. This provides an analogue of de Vries duality for proximity Baer Specker A-algebras.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 219, Issue 9, September 2015, Pages 3958–3991
نویسندگان
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