An Extension of the Stone Duality |
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Authors: | M Sonia P Sabogal |
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Institution: | (1) Escuela de Matemáticas, Universidad Industrial de Santander, A.A. 678, Bucaramanga, Colombia, S.A. |
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Abstract: | We establish a duality between two categories, extending the Stone duality between totally disconnected compact Hausdorff
spaces (Stone spaces) and Boolean rings with a unit. The first category denoted by RHQS, has as objects the representations
of Hansdorff quotients of Stone spaces and as morphisms all compatible continuous functions. The second category, denoted
by BRLR, has as objects all Boolean rings with a unit endowed with a link relation and as morphisms all compatible Boolean
rings with unit morphisms. Furthermore, we study connectedness from an algebraic point of view, in the context of the proposed
generalized Stone duality.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | |
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