Fuzzy topologies and topological space objects in a topos
Fuzzy Sets and Systems
Abstract and concrete categories
Abstract and concrete categories
Point-set lattice-theoretic topology
Fuzzy Sets and Systems - Special memorial volume on mathematical aspects of fuzzy set theory
Fuzzy Sets and Systems - Special issue on fuzzy topology
A general theory of fuzzy topological spaces
Fuzzy Sets and Systems - Special issue on fuzzy topology
Handbook of logic in computer science (vol. 3)
Sobriety and spatiality in varieties of algebras
Fuzzy Sets and Systems
Pointed semi-quantales and lattice-valued topological spaces
Fuzzy Sets and Systems
Overview and comparison of localic and fixed-basis topological products
Fuzzy Sets and Systems
Generalized fuzzy topology versus non-commutative topology
Fuzzy Sets and Systems
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It is shown in this paper that various approaches to fuzzy topological spaces can be extended to an abstract category C. In this respect, variety-based generalized topological spaces, variable-basis fuzzy topological spaces, fixed-basis fuzzy topological spaces and Hutton fuzzy topological spaces are defined in C. We also construct their respective categories, as well as establish a generalized Papert-Papert-Isbell style adjunction for each of them. These adjunctions are later on refined to equivalences, involving appropriate definitions of spatiality and sobriety.