Epimorphisms and cowellpoweredness for separated metrically generated theories
The paper presents new results about metrically generated theories, compare \textit{E. Colebunders} and \textit{R. Lowen} [Proc. Am. Math. Soc. 133, 1547--1556 (2005; Zbl 1073.54006)]). For metrically generated constructs \(\mathbb X\) the authors give an internal characterization of the regular closure operator on \(\mathbb X,\) determined by the subconstruct \(\mathbb X_0\), consisting of its \(T_0\) objects. That result is then used to describe the epimorphisms in \(\mathbb X_0\) and to prove that all constructs of that type are cowellpowered. The methods lead to some new results (for instance a characterization of the epis in \(\mathbb A\mathbb P_0\), where \(\mathbb A\mathbb P\) denotes the construct of approach spaces), besides unifying many known cases.
scientific article; zbMATH DE number 5150257