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Information Journal Paper

Title

CATEGORICALLY-ALGEBRAIC TOPOLOGY AND ITS APPLICATIONS

Pages

  57-94

Abstract

 This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of LATTICE-VALUED TOPOLOGY, including poslat topology of S. E. Rodabaugh, (L; M)-fuzzy topology of T. Kubiak and A. Sostak, andM-fuzzy topology on L-fuzzy sets of C. Guido.Moreover, its respective categories of topological structures are topological over their ground categories. The theory also extends the notion of TOPOLOGICAL SYSTEM of S. Vickers (and its numerous many-valued modifications of J. T. Denniston, A. Melton and S. E. Rodabaugh), and shows that the categories of catalg topological structures are isomorphic to coreective subcategories of the categories of catalg TOPOLOGICAL SYSTEMs. This extension initiates a new approach to SOFT TOPOLOGY, induced by the concept of soft set of D. Molodtsov, and currently pursued by various researchers.

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    • Cite

    APA: Copy

    SOLOVYOV, S.A.. (2015). CATEGORICALLY-ALGEBRAIC TOPOLOGY AND ITS APPLICATIONS. IRANIAN JOURNAL OF FUZZY SYSTEMS, 12(3), 57-94. SID. https://sid.ir/paper/703439/en

    Vancouver: Copy

    SOLOVYOV S.A.. CATEGORICALLY-ALGEBRAIC TOPOLOGY AND ITS APPLICATIONS. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2015;12(3):57-94. Available from: https://sid.ir/paper/703439/en

    IEEE: Copy

    S.A. SOLOVYOV, “CATEGORICALLY-ALGEBRAIC TOPOLOGY AND ITS APPLICATIONS,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 12, no. 3, pp. 57–94, 2015, [Online]. Available: https://sid.ir/paper/703439/en

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