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Abstract
By means of the residual implication on a frame L, a degree approach to L-continuity and L-closedness for mappings between L-cotopological spaces are defined and their properties are investigated systematically. In addition, in the situation of L-topological spaces, degrees of L-continuity and of L-openness for mappings are proposed and their connections are studied. Moreover, if L is a frame with an order-reversing involution ′ , where b ′ = b → ⊥ for b ∈ L , then degrees of L-continuity for mappings between L-cotopological spaces and degrees of L-continuity for mappings between L-topological spaces are equivalent.
Highlights
Since Chang [1] introduced fuzzy set theory to topology, fuzzy topology and its related theories have been widely investigated such as [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]
We equip each mapping between L-cotopological spaces with some degree to be an L-continuous mapping and an L-closed mapping, and equip each mapping between
L-topological spaces with some degree to be an L-continuous mapping and an L-open mapping
Summary
Since Chang [1] introduced fuzzy set theory to topology, fuzzy topology and its related theories have been widely investigated such as [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18]. The degree approach that equips fuzzy topology and its related structures with some degree description is an essential character of fuzzy set theory This approach has been developed extensively in the theory of fuzzy topology, fuzzy convergence and fuzzy convex structure. Special mappings between structured spaces and the structured space itself can be endowed with some degrees Xiu and his co-authors [25,26] defined degrees of fuzzy convex structures, fuzzy closure systems and fuzzy Alexandrov topologies and discussed their properties. By means of L-closure operators and L-interior operators, we will consider degrees of L-continuity and L-closedness for mappings between L-cotopological spaces as well as degrees of L-continuity and L-openness for mappings between L-topological spaces and will investigate their properties systematically
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