Generalized topologies with associating function and logical applications

  • Tomasz Witczak University of Silesia
Keywords: Generalized topology, modal logic, convergence spaces, nets and sequences


The whole universe of a generalized topological space may not be open. Hence, some points may be beyond any open set. In this paper we assume that such points are associated with certain open neighbourhoods by means of a special function F. We study various properties of the structures obtained in this way. We introduce the notions of F-interior and F-closure and we discuss issues of convergence in this new setting. It is possible to treat our spaces as a semantical framework for modal logic.


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Author Biography

Tomasz Witczak, University of Silesia

Institute of Mathematics, Faculty of Science and Technology