Generalized Lowen functors

Publication Type:
Journal Article
Citation:
Fuzzy Sets and Systems, 2003, 133 (3), pp. 375 - 387
Issue Date:
2003-02-01
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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 ι. 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 ωfand ιfbetween L1-TOP and L2-TOP for each Scott continuous mapping f: L2→ L1, where L1and L2are 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 ιf(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(Δ) is the finest Lowen topology on X contained in Δ and ιf(Δ) is the coarsest Lowen topology on X containing Δ, etc. © 2002 Elsevier Science B.V. All rights reserved.
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