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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