Topological systems versus attachment relations

  • Cosimo Guido
  • Sergey A Solovyov


The manuscript makes a category-theoretic comparison between the concepts of topological system of S. Vickers and attachment relation of C. Guido. With the help of the recent definition of the notions in the framework of an arbitrary variety of algebras, we consider functorial relationships between the categories of such generalized structures, and the link of the obtained functors to both spatialization and localification procedure introduced by S. Vickers for topological systems.

Keywords: Adjoint functor, algebra, attachment relation, embedding functor, localification of topological systems, spatialization of topological systems, topological system, topological theory, variety of algebras

Quaestiones Mathematicae 37(2014), 455-484

Author Biographies

Cosimo Guido
Department of Mathematics “Ennio De Giorgi”, University of Salento, P.O. Box 193, 73100 Lecce, Italy
Sergey A Solovyov
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic, and Institute of Mathematics and Computer Science, University of Latvia, Raina bulvaris 29, LV-1459 Riga, Latvia

Journal Identifiers

eISSN: 1727-933X
print ISSN: 1607-3606