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ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 6، دوره 10، شماره 3، شهریور 2013، صفحه 65-102 اصل مقاله (607.36 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2013.863 | ||
نویسندگان | ||
Anna Frascella1؛ Cosimo Guido2؛ Sergey A. Solovyov ![]() ![]() | ||
1Department of Mathematics E. De Giorgi", University of Salento, P. O. Box 193, 73100 Lecce, Italy | ||
2Department of Mathematics E. De Giorgi", University of Salento, P. O. Box 193, 73100 Lecce, Italy | ||
3Department 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 | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
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 | ||
مراجع | ||
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