ISSN:
1572-9095
Keywords:
quasi-uniform space
;
uniform space
;
(regular
;
semiregular) closure operator
;
θ-closure
;
sequential closure
;
S(α)-space
;
ϱ-separated space
;
epimorphism
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We study some categorical aspects of quasi-uniform spaces (mainly separation and epimorphisms) via closure operators in the sense of Dikranjan, Giuli, and Tholen. In order to exploit better the corresponding properties known for topological spaces we describe the behaviour of closure operators under the lifting along the forgetful functor T from quasi-uniform spaces to topological spaces. By means of appropriate closure operators we compute the epimorphisms of many categories of quasi-uniform spaces defined by means of separation axioms and study the preservation (reflection) of epimorphisms under the functor T.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008743408583
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