Pre-topologies and Dynamic Spaces [chapter]

Piero Pagliani
Lecture Notes in Computer Science  
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
more » ... 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.
doi:10.1007/3-540-39205-x_19 dblp:conf/rsfdgrc/Pagliani03 fatcat:nqsngqwzhrazhj5ibw6gf3edbi