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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

4 Issues per year

SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

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Volume 24, Issue 3


Uniform Space

Roland Coghetto
Published Online: 2017-02-21 | DOI: https://doi.org/10.1515/forma-2016-0018


In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2].

We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group.

Next, we define the concept of the partition topology. Following the Vlach’s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence relation.

Finally, using mostly Gehrke, Grigorieff and Pin [4] works, a Pervin uniform space defined from the sets of the form ((X\A) × (X\A)) ∪ (A×A) is presented.

MSC: 54E15; 03B35

Keywords: uniform space; uniformity; pseudo-metric space; topological group; partition topology; Pervin uniform space

MML: identifier: UNIFORM3; version: 8.1.05 5.37.1275


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About the article

Received: 2016-06-30

Published Online: 2017-02-21

Published in Print: 2016-09-01

Citation Information: Formalized Mathematics, Volume 24, Issue 3, Pages 215–226, ISSN (Online) 1898-9934, DOI: https://doi.org/10.1515/forma-2016-0018.

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© by Roland Coghetto. This work is licensed under version 3.0 of the Creative Commons Attribution–ShareAlike License BY-SA 3.0 LEGALCODE

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