ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS

Document Type: Research Paper

Authors

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

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

3 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

Abstract

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.

Keywords


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