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ON CERTAIN FACTORIZATIONS OF FUNCTORS INTO THE CATEGORY OF QUASI-UNIFORM SPACES

 

作者: G.C.L. Brümmer,  

 

期刊: Quaestiones Mathematicae  (Taylor Available online 1977)
卷期: Volume 2, issue 1-3  

页码: 59-84

 

ISSN:1607-3606

 

年代: 1977

 

DOI:10.1080/16073606.1977.9632534

 

出版商: Taylor & Francis Group

 

关键词: Primary 18A99;54B99;54E15;54E55;secondary 18D99;54D30;Right inverse of forgetful functor;odd functor;quasi-uniform space;bitopological space;transitive quasi-uniformity

 

数据来源: Taylor

 

摘要:

This paper is motivated by the search for natural extensions of classical uniform space results to quasi-uniform spaces. As instances of such extensions we restate some theorems of P. Fletcher and W.F. Lindgren [Pacific J. Math. 43 (1971), 619–6311 on transitive quasi-uniformities and of S. Salbany [Thesis, Univ. Cape Town, 1971] on compactification and completion. The theorems as restated describe properties of certain right inverses of the functor which forgets the quasi-uniform structure and retains one induced topology (for Fletcher and Lindgren's work), respectively retains both induced topologies (for Salbany's work). Accordingly we investigate systematically the process by which the right inverses of the forgetful functors can be extended from the classical setting to one of these settings, and from one of these to the other.

 

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