ALGEBRAICALLY-TOPOLOGICAL SYSTEMS AND ATTACHMENTS

作者：Frascella A; Guido C; Solovyov S A^*

来源：Iranian Journal of Fuzzy Systems, 2013, 10(3): 65-102.

• 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

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.

• 出版日期2013-6