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Algebre di Fréchet: Una classe di Algebre booleane con operatore

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Summary

A Closure Algebra is a Boolean algebraA together with an operatorK:A→A satisfying the formal properties of the closure operator of a topological space. A generalization of this concept is that of “F-algebra”, a Boolean algebraA with an operatorK satisfying only the two axioms of a “generalized topological space” (Appert), namelyK 0=0 and x≤Kx, ∈A. We try to extend to F-algebras some of the results of point-set topology.

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Bibliografia

  1. Appert A. e Fan K.,Espaces topologiques intermediaires.Problème de la distanciation, Actualités Sci. Ind. no. 1121. Hermann & Cie., Paris, 1951.

    MATH  Google Scholar 

  2. Bourbaki N.,Éléments de mathématique. 22 Première partie: Les structures fondamentales de l’analyse. Livre 1: Théorie des ensembles. Chapitre 4: Structures, Actualités Sci. Ind. no. 1258. Hermann, Paris, 1957.

    Google Scholar 

  3. Geymonat L.,La spazializzazione degli insiemi, Univ. e Politec. Torino, Rend. Sem. Mat. Fis.13 (1954), 47–58.

    MathSciNet  Google Scholar 

  4. Geymonat L.,Su di un metodo per lo studio di spazi astratti molto generali, Univ. Roma, 1st. Naz. Alta Mat. Rend. Mat. e Appl. (5)12 (1953), 360–363 (1954).

    MathSciNet  Google Scholar 

  5. Geymonat L.,Sulla combinazione di due caratteristiche trasformazioni della contiguità negli spazi topologici, Univ. Roma, Ist. Naz. Alta Mat. Rend. Mat. e Appl. (5)14 (1954), 200–208.

    MATH  MathSciNet  Google Scholar 

  6. Halmos P. R.,Lectures on Boolean algebras, Van Nostrand Mathematical Studies n. 1, New York, 1963.

  7. Magari R. e Mangani P.,Alcune osservazioni sugli assiomi delle “algebre monadiche” di Halmos, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur.98 (1963/64), 265–278.

    MathSciNet  Google Scholar 

  8. Magari R. e Mangani P.,Sulle topologie “compatibili” con una data algebra monadica, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur.98 (1963/64), 299–314.

    MathSciNet  Google Scholar 

  9. McKinsey J. C. C. e Tarski A.,The Algebra of Topology, Ann. of Math. (2)45 (1944), 141–191.

    Article  MathSciNet  Google Scholar 

  10. Rasiowa H. e Sikorski R.,The mathematics of metamathematics, Monografie Matematyczne, Tom 41. Państwowe Wydawnictwo Naukowe, Warsaw, 1963.

    MATH  Google Scholar 

  11. Servi M.,Sulla meno fine topologia ottenuta per estensione da una infratopologia generalizzata, Univ. e Politec. Torino, Rend. Sem. Mat. Fis.23 (1963/64), 237–248.

    MathSciNet  Google Scholar 

  12. Sikorski R.,Boolean Algebras, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Band 25. Springer-Verlag, Berlin-Göttingen-Heidelberg-New York, 1964.

    MATH  Google Scholar 

  13. Sikorski R.,Closure Algebras, Fund. Math.36 (1949), 165–206.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Parma, Italia

    Mario Servi

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  1. Mario Servi
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Lavoro eseguito nell’ambito dell’attività del Gruppo di Ricerca n. 37 del Comitato per la Matematica del C. N. R. per l’anno 1965–66.

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Servi, M. Algebre di Fréchet: Una classe di Algebre booleane con operatore. Rend. Circ. Mat. Palermo 14, 335–366 (1965). https://doi.org/10.1007/BF02844036

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