Observations on quasi-uniform products (Q870245)

The article is devoted to quasi-uniform spaces. Theorems about products of quasi-uniform spaces and their quotient mappings are proved. Their relations with quasi-proximity spaces are studied. Examples illustrating these spaces are given. Definitions, notations and results from the book [\textit{P. Fletcher} and \textit{W. F. Lindgren}, Quasi-uniform spaces. New York, Basel: Marcel Dekker (1982; Zbl 0501.54018)] are actively used. The authors of the paper demonstrate that a product of quotient maps in the category of quasi-uniform spaces and quasi-uniformly continuous maps is a quotient map. The particular case when a quasi-uniformly continuous map from a product of quasi-uniform spaces into a quasi-metric \(T_0\) space depends on countably many coordinates is elucidated.