Pretopologies and dynamic spaces

  • Authors:

  • Piero Pagliani

  • Affiliations:

  • Research Group on Knowledge and Communication Models, Via Imperia, 6. 00161 Rome, Italy

  • Venue:
  • Fundamenta Informaticae - Special issue on the 9th international conference on rough sets, fuzzy sets, data mining and granular computing (RSFDGrC 2003)
  • Year:
  • 2003

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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 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, {Ri}i∈I 〈, where {Ri}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.