Generalized topologies with associating function and logical applications | Zendy

Tomasz Witczak | Zendy

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Generalized topologies with associating function and logical applications

Author(s) -

Tomasz Witczak

Publication year - 2020

Publication title -

acta et commentationes universitatis tartuensis de mathematica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.276

H-Index - 6

eISSN - 2228-4699

pISSN - 1406-2283

DOI - 10.12697/acutm.2020.24.17

Subject(s) - closure (psychology) , convergence (economics) , function space , topological space , function (biology) , set (abstract data type) , modal logic , open set , mathematics , space (punctuation) , universe , modal , computer science , topology (electrical circuits) , network topology , pure mathematics , theoretical computer science , discrete mathematics , combinatorics , physics , programming language , chemistry , evolutionary biology , economics , polymer chemistry , astrophysics , market economy , biology , economic growth , operating system

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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