Generalized Lowen functors

Li, S; Luo, M

Generalized Lowen functors

Li, S

Luo, M

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Publication Type:: Journal Article
Citation:: Fuzzy Sets and Systems, 2003, 133 (3), pp. 375 - 387
Issue Date:: 2003-02-01

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Field	Value	Language
dc.contributor.author	Li, S https://orcid.org/0000-0002-3332-2546	en_US
dc.contributor.author	Luo, M	en_US
dc.date.issued	2003-02-01	en_US
dc.identifier.citation	Fuzzy Sets and Systems, 2003, 133 (3), pp. 375 - 387	en_US
dc.identifier.issn	0165-0114	en_US
dc.identifier.uri	http://hdl.handle.net/10453/9077
dc.description.abstract	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 ωf and ιf 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 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.	en_US
dc.relation.ispartof	Fuzzy Sets and Systems	en_US
dc.relation.isbasedon	10.1016/S0165-0114(02)00384-6	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Generalized Lowen functors	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	133	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Strength - QSI - Centre for Quantum Software and Information
utslib.copyright.status	closed_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	133	en_US

Abstract:

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 ωf and ιf 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 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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http://hdl.handle.net/10453/9077