Approximation Spaces and Nearness Type Structures

Issue title: Special Issue on Concurrency Specification and Programming (CS&P)

Article type: Research Article

Authors: Wolski, Marcin

Affiliations: Department of Logic and Methodology of Science, Maria Curie-Skłodowska University, Poland. E-mail: [email protected]

Abstract: The present paper investigates approximation spaces in the context of mathematical structures which axiomatise the notion of nearness. Starting with the framework of information quanta which distinguishes two levels of information structures, namely property systems (the first level) and information quantum relational systems (the second level), we shall introduce the notion of Pawlak property system. These systems correspond bijectively to finite approximation spaces, i.e. their respective information quantum relational systems. Then we characterise Pawlak property systems in terms of symmetric topological spaces. In the second part of the paper, these systems are defined by means of topological structures based on the concept of nearness. We prove that the category of Pawlak property systems is isomorphic to the category of finite topological nearness spaces and provide its additional topological characterisation.

Journal: Fundamenta Informaticae, vol. 79, no. 3-4, pp. 567-577, 2007