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Formalized Mathematics

(a computer assisted approach)

Editor-in-Chief: Matuszewski, Roman

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SCImago Journal Rank (SJR) 2016: 0.207
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Volume 24, Issue 3


Quasi-uniform Space

Roland Coghetto
Published Online: 2017-02-21 | DOI: https://doi.org/10.1515/forma-2016-0017


In this article, using mostly Pervin [9], Kunzi [6], [8], [7], Williams [11] and Bourbaki [3] works, we formalize in Mizar [2] the notions of quasiuniform space, semi-uniform space and locally uniform space.

We define the topology induced by a quasi-uniform space. Finally we formalize from the sets of the form ((X \ Ω) × X) ∪ (X × Ω), the Csaszar-Pervin quasi-uniform space induced by a topological space.

MSC: 54E15; 03B35

Keywords: quasi-uniform space; quasi-uniformity; Pervin space; Csaszar-Pervin quasi-uniformity

MML: identifier: UNIFORM2; 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 205–214, ISSN (Online) 1898-9934, DOI: https://doi.org/10.1515/forma-2016-0017.

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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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