(IC) L-cotopological spaces

Authors:
Sheng-Gang Li;Hai-Yang Li;Wen-Qing Fu
Affiliations:
College of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi'an, PR China;College of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi'an, PR China and Xi'an University of Engineering Science and Technology, 710049 Xi'an, China;College of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi'an, PR China
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

The aim of this paper is to define and study (IC) L-cotopological spaces, a generalization of Martin's weakly induced I-topological spaces (particularly, Weiss's induced spaces and Lowen's topologically generated spaces). Under a moderate restriction to L, we prove that ICLTop^c (the category of (IC) L-cotopological spaces and continuous mappings) is an isomorphism-closed full proper subcategory of LTop^c (the category of L-cotopological spaces and continuous mappings) which is simultaneously bireflective and bicoreflective in LTop^c, and that an L-cotopological space (X,@d) is an (IC) space if and only if its induced I(L)-cotopological space (X,@W"L^o^p(@d)) is an (IC) space.