Lebesgue Property and $G$-completeness in Generalized Quasi-uniform Spaces

Abstract

This paper extends the Lebesgue property and (weak) $G$-completeness to generalized quasi-uniform spaces. It investigates the connections between completeness, (weak) $G$-completeness, and the Lebesgue property of the product of generalized quasi-uniform spaces with those of the component spaces. It has been observed that the related behaviors differ for the Lebesgue property in contrast to completeness and (weak) $G$-completeness.