Volume 12, 2000

University of Bialystok

Copyright (c) 2000 Association of Mizar Users

**Mariusz Giero**- University of Bialystok
**Roman Matuszewski**- University of Bialystok

- The paper introduces some preliminary notions concerning the Wroclaw taxonomy according to [14]. The classifications and tolerances are defined and considered w.r.t. sets and metric spaces. We prove theorems showing various classifications based on tolerances.

This work has been partially supported by the European Community TYPES grant IST-1999-29001 and CALCULEMUS grant HPRN-CT-2000-00102.

- Preliminaries
- The Notion of Classification
- The Tolerance on a Non Empty Set
- The Partitions Defined by Lower Tolerance
- The Classification on a Non Empty Set
- The Classification on a Metric Space

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