Local metrically generated theoriesLocal metrically generated theories
Faculty of Sciences. Mathematics and Computer Science
Analytical and topological structures
Topology and its applications. - Amsterdam
159(2012):9, p. 2320-2330
University of Antwerp
In this paper we prove that for every metrically generated theory (Colebunders and Lowen, 2005 ) there exists a largest, what we call local metrically generated theory underlying it. We illustrate this result by looking at the traditional case of the categories of topological spaces and quasi-uniform spaces (Künzi, 2001 ) and also by looking at the categories of approach spaces (Lowen, 1997 ) and quasi-uniform gauge spaces (Lowen, 2004 ) and some of their usual sub- and supercategories (Choquet, 1948 ; Colebunders and Lowen, 1989 ; Herrlich, 1987 ; Preuss, 1988 ).