Fuzzy algebras as a framework for fuzzy topology

The paper introduces a variety-based version of the notion of the (L,M)-fuzzy topological space of Kubiak and Šostak and embeds the respective category into a suitable modification of the category of topological systems of Vickers. The new concepts provide a common framework for different approaches to fuzzy topology and topological systems existing in the literature, paving the way for studying the problem of interweaving algebra and topology in mathematics, which was raised by Denniston, Melton and Rodabaugh in their recent research on variable-basis topological systems over the category of locales.