Uniform Space

• Autorzy: Roland Coghetto
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2016
• Tom: 24
• Numer: 3
• Strony: 215-226

Daty

wydano

2016-09-01

otrzymano

2016-06-30

online

2017-02-08

Twórcy

autor

Roland Coghetto

• Rue de la Brasserie 5 7100 La Louvière,

Identyfikatory

DOI

10.1515/forma-2016-0018