Pre-topologies and dynamic spaces

Authors:
Piero Pagliani
Affiliations:
Research Group on Knowledge and Communication Models, Rome, Italy
Venue:
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
Year:
2003

Citing 2
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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 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 to 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.