Point-Free Version of Kakutani Duality |
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Authors: | A?Karimi Feizabadi Email author" target="_blank">M?M?EbrahimiEmail author |
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Institution: | (1) Department of Mathematics, Islamic Azad University, Gorgan, Iran;(2) Department of Mathematics, Shahid Beheshti University, Tehran, 19839, Iran |
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Abstract: | There are many results proved using the Axiom of Choice. Using point-free topology, we can prove some of these results without
using this axiom. B. Banaschewski in Pointfree Topology and the Spectra of f-rings, Ordered algebraic structures (Curacoa, 1995), Kluwer, Dordrecht, 123–148], studying the spectra of f-rings, describes the point-free version of the classical Gelfand duality without using the Axiom of Choice In this paper,
referring to Ebrahimi, M. M., Karimi Feizabadi, A. and Mahmoudi, M.: Pointfree Spectra of Riesz Space, Appl. Categ. Struct.
12 (2004), 397–409; Ebrahimi, M. M. and Karimi Feizabadi, A.: Pointfree Spectra of ℓ-Modules, To appear in J. Pure Appl. Algebra], we describe a point-free version of the classical Kakutani duality. For this, using one of the spectra given in Ebrahimi,
M. M., Karimi Feizabadi, A. and Mahmoudi, M.: Pointfree Spectra of Riesz Space, Appl. Categ. Struct.
12 (2004), 397–409; Ebrahimi, M. M. and Karimi Feizabadi, A.: Pointfree Spectra of l-Modules, To appear in J. Pure Appl. Algebra], we find an adjunction between the category of compact completely regular frames with
frame maps and the category of Archimedean bounded Riesz spaces with continuous Riesz maps. |
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Keywords: | 06D22 46A40 46B40 46B42 03E25 03E99 |
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