Journal of Formalized Mathematics
Volume 12, 2000
University of Bialystok
Copyright (c) 2000 Association of Mizar Users

Lower Tolerance. Preliminaries to Wroclaw Taxonomy


Mariusz Giero
University of Bialystok
Roman Matuszewski
University of Bialystok

Summary.

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.

MML Identifier: TAXONOM1

The terminology and notation used in this paper have been introduced in the following articles [18] [8] [20] [2] [19] [7] [21] [23] [5] [22] [6] [13] [16] [12] [11] [10] [17] [3] [4] [15] [1] [9]

Contents (PDF format)

  1. Preliminaries
  2. The Notion of Classification
  3. The Tolerance on a Non Empty Set
  4. The Partitions Defined by Lower Tolerance
  5. The Classification on a Non Empty Set
  6. The Classification on a Metric Space

Acknowledgments

The authors thank Prof. Andrzej Trybulec for his introduction to this topic. We thank Dr. Artur Kornilowicz for his advice on this article. We also thank Robert Milewski and Adam Naumowicz for their helpful comments.

Bibliography

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Received December 5, 2000


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