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Iranian Journal of Fuzzy Systems، جلد ۱۰، شماره ۳، صفحات ۶۵-۱۰۲
عنوان فارسی ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS
چکیده فارسی مقاله The paper continues the study of the authors on relationships between emph{topological systems} of S.~Vickers and emph{attachments} of C.~Guido. We extend topological systems to emph{algebraically-topological systems}. A particular instance of the latter, called emph{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.
کلیدواژه‌های فارسی مقاله Algebraically-topological system، Attachment system، Categorically-algebraic topology، Dual attachment pair، Localic algebra، Localification of systems، (Variety-based) pointless topology، Spatialization of systems، Topological theory morphism، Variety،
عنوان انگلیسی ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS
چکیده انگلیسی مقاله The paper continues the study of the authors on relationships between emph{topological systems} of S.~Vickers and emph{attachments} of C.~Guido. We extend topological systems to emph{algebraically-topological systems}. A particular instance of the latter, called emph{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.
کلیدواژه‌های انگلیسی مقاله Algebraically-topological system, Attachment system, Categorically-algebraic topology, Dual attachment pair, Localic algebra, Localification of systems, (Variety-based) pointless topology, Spatialization of systems, Topological theory morphism, Variety
نویسندگان مقاله Anna Frascella |
Department of Mathematics E. De Giorgi", University of Salento, P. O. Box 193, 73100 Lecce, Italy

Cosimo Guido |
Department of Mathematics E. De Giorgi", University of Salento, P. O. Box 193, 73100 Lecce, Italy

Sergey A. Solovyov |
Department of Mathematics, University of Latvia, Zellu iela 8, LV-1002 Riga, Latvia and Institute of Mathematics and Computer Science, University of Latvia, Raina bulvaris 29, LV-1459 Riga, Latvia

نشانی اینترنتی http://ijfs.usb.ac.ir/article_863_f7926f99d233d0b927339f4338ddbc5c.pdf
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