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 the universe of data and E is an equivalence relation on U . Various authors suggested considering spaces of the form U, R , where R is any relation. This paper aims at introducing a further step consisting in spaces of the form U, {R} i∈I , where {R} i∈I is a family of relations on U , that we call "Dynamic Spaces", because they make it possible

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... 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.