Uniform Space

Pole DC	Wartość	Język
dc.contributor.author	Coghetto, Roland	-
dc.date.accessioned	2017-06-02T11:53:01Z	-
dc.date.available	2017-06-02T11:53:01Z	-
dc.date.issued	2016	-
dc.identifier.citation	Formalized Mathematics, Volume 24, Issue 3, pp. 215-226	pl
dc.identifier.issn	1426-2630	pl
dc.identifier.issn	1898-9934	pl
dc.identifier.uri	http://hdl.handle.net/11320/5556	-
dc.description.abstract	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.	-
dc.language.iso	en	-
dc.publisher	De Gruyter Open	-
dc.subject	uniform space	-
dc.subject	uniformity	-
dc.subject	pseudo-metric space	-
dc.subject	topological group	-
dc.subject	partition topology	-
dc.subject	Pervin uniform space	-
dc.title	Uniform Space	-
dc.type	Article	-
dc.identifier.doi	10.1515/forma-2016-0018	-
dc.description.Affiliation	Rue de la Brasserie 5 7100 La Louvière, Belgium	-
dc.description.references	Grzegorz Bancerek, Czesław Bylinski, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pak, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261-279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1.	-
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dc.description.references	Milan Vlach. Algebraic and topological aspects of rough set theory. In Fourth International Workshop on Computational Intelligence & Applications, IEEE SMC Hiroshima Chapter, Hiroshima University, Japan, December 10&11, 2008.	-
dc.description.references	Milan Vlach. Topologies of approximation spaces of rough set theory. In Interval/ Probabilistic Uncertainty and Non-Classical Logics, pages 176-186. Springer, 2008.	-
Występuje w kolekcji(ach):	Formalized Mathematics, 2016, Volume 24, Issue 3

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