ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS

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FRASCELLA ANNA; GUIDO COSIMO; SOLOVYOV S.A.

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Paper Information

Journal: Iranian Journal of Fuzzy Systems Year:2013 | Volume:10 | Issue:3 Page(s): 65-102

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Information Journal Paper

Title

ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS

Author(s)

FRASCELLA ANNA | GUIDO COSIMO | SOLOVYOV S.A. | Issue Writer Certificate

Keywords

ALGEBRAICALLY-TOPOLOGICAL SYSTEM

ATTACHMENT SYSTEM

CATEGORICALLY ALGEBRAIC TOPOLOGY

DUAL ATTACHMENT PAIR

LOCALIC ALGEBRA

LOCALIFICATION OF SYSTEMS

(VARIETYBASED) POINTLESS TOPOLOGY

SPATIALIZATION OF SYSTEMS

TOPOLOGICAL THEORY MORPHISM

VARIETY

Abstract

The paper continues the study of the authors on relationships between topological systems of S. Vickers and attachments of C. Guido. We extend topological systems to ALGEBRAICALLY-TOPOLOGICAL SYSTEMs. A particular instance of the latter, called ATTACHMENT SYSTEM, incorporates the notion of attachment, thus, making it categorically redundant in mathematics. We show that ATTACHMENT SYSTEMs are equipped with an internal topology, which is similar to the topology induced by locales. In particular, we provide an ATTACHMENT SYSTEM analogue of the well-known categorical equivalence between sober topological spaces and spatial locales.

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APA: Copy

FRASCELLA, ANNA, GUIDO, COSIMO, & SOLOVYOV, S.A.. (2013). ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS. IRANIAN JOURNAL OF FUZZY SYSTEMS, 10(3), 65-102. SID. https://sid.ir/paper/604524/en

Vancouver: Copy

FRASCELLA ANNA, GUIDO COSIMO, SOLOVYOV S.A.. ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS. IRANIAN JOURNAL OF FUZZY SYSTEMS[Internet]. 2013;10(3):65-102. Available from: https://sid.ir/paper/604524/en

IEEE: Copy

ANNA FRASCELLA, COSIMO GUIDO, and S.A. SOLOVYOV, “ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS,” IRANIAN JOURNAL OF FUZZY SYSTEMS, vol. 10, no. 3, pp. 65–102, 2013, [Online]. Available: https://sid.ir/paper/604524/en

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