Hutton L-double uniform spaces

Abstract

We introduce the concept of L-double uniform spaces in Hutton’s sense. We prove the category of L-double uniform spaces is topological category over SET. The natural relationships between L-double uniformities, L-double fuzzy topologies and L-double fuzzy topogenous structures are studied. The family $\coprod(\eta,\eta^{*})$ of all L-double uniformities $(\mathcal{U},\mathcal{U}^{*})$ compatible with an L-double fuzzy topogenous structure (η, η^*) on X is never empty and it contains an L-double uniformity $(\mathcal{U}_{\eta},\mathcal{U}_{\eta^{*}})$, which is the coarsest member of $\coprod(\eta,\eta^{*}).$