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
Galois connections between categories of L-topological spaces
Fuzzy Sets and Systems
On the uniformization of lattice-valued frames
Fuzzy Sets and Systems
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According to their value ranges, L-topological spaces form different categories. Clearly, the investigation on their relationships is certainly important and necessary. Lowen was one of the first authors who had studied the relation between the category of I-topological spaces and that of topological spaces. He introduced two well-known functors: ω and i. Later, these functors, namely Lowen functors, were extended by different authors for various kinds of lattices studying the relation between L-TOP and TOP. In this paper, we introduce two functors ωf and if between L1-TOP and L2-TOP for each Scott continuous mapping f : L2 → L1, where L1 and L2 are arbitrary two completely distributive lattices. Some topological properties related to these functors are revealed, e.g., for Li-topological space (Xi,Δi) (i = 1,2), both ωf(X1,Δ1) and if(X2,Δ2) are Lowen spaces; in the case that f is the identity mapping on a linearly ordered complete lattice, for L-topological space (X,Δ), ωf(Ω) is the finest Lowen topology on X contained in Δ and if(Δ) is the coarsest Lowen topology on X containing Δ, etc.