Pretopologies and Dynamic Spaces

Abstract

Approximation Spaces were introduced in order to analyse data on the basis of Indiscernibility Spaces, that is, spaces of the form <U,E>, where U is a universe of items and E is an equivalence relation on U. Various authors suggested to consider spaces of the form <U,R>, where R is any binary relation. This paper aims at introducing a further step consisting in taking into account spaces of the form <U,{R_i}_{i∈I}>, where {R_i}_{i∈I} is a family of binary relations, that we call „Dynamic Spaces” because by means of this generalisation we can account for different forms of dynamics. While Indiscernibility Spaces induce 0-dimensional topological spaces (Approximation Spaces), Dynamic Spaces induce various types of pre-topological spaces.