A characterization of rough separability

  • Authors:

  • Piotr Wasilewski;Andrzej Skowron

  • Affiliations:

  • Institute of Informatics, The University of Warsaw, Warsaw, Poland;Institute of Mathematics, The University of Warsaw, Warsaw, Poland

  • Venue:
  • RSKT'12 Proceedings of the 7th international conference on Rough Sets and Knowledge Technology
  • Year:
  • 2012

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Abstract

Rough separability in topology is discussed by its connections with pseudometric spaces and rough sets. Pseudometric spaces are presented from the point of view of their connections with approximation spaces. A special way of determining equivalence relations by pseudometric spaces is considered and open sets in pseudometric spaces are studied. Investigations focus on the class of pseudometric spaces which are lower bounded in each point since open sets in these spaces coincide with definable sets of some prescribed approximation spaces. It is also shown that all equivalence and non transitive tolerance relations can be determined by pseudometric spaces in specified ways.