Similarity as Nearness: Information Quanta, Approximation Spaces and Nearness Structures

The present paper investigates approximation spaces in the context of topological 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’s property system. These systems correspond bijectively to finite approximation spaces, i.e. their respective information quantum relational systems. Then we characerise Pawlak’s 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’s property systems is isomorphic to the category of finite topological nearness spaces and provide its additional topological characterisation.