(IC) L-cotopological spaces

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 ICLTopc (the category of (IC) L-cotopological spaces and continuous mappings) is an isomorphism-closed full proper subcategory of LTopc (the category of L-cotopological spaces and continuous mappings) which is simultaneously bireflective and bicoreflective in LTopc, and that an L-cotopological space (X,δ) is an (IC) space if and only if its induced I(L)-cotopological space is an (IC) space.