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2008•Journal of Shandong UniversityRequires access

F*-Paracompactness in L-topological spaces

Meng Guang-wu

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Abstract

F*-paracompactness in L-topological spaces was introduced.It was proved that F*-paracompactness has many good properties,such as that it is L-good extension,hereditary with respect to closed subsets,weakly in homeomorphic invariant property,and that the Cartesian product of a fuzzy compact space and a F*-paracompact space is a F*-paracompact space,as well as that a F*-paracompact Hausdorff space is both a S*-regular and a WS*-normal space.At last,a discussion about the relations of other paracompactnesses was given.

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F*-paracompactness in L-topological spaces was introduced.It was proved that F*-paracompactness has many good properties,such as that it is L-good extension,hereditary with respect to closed subsets,weakly in homeomorphic invariant property,and that the Cartesian product of a fuzzy compact space and a F*-paracompact space is a F*-paracompact space,as well as that a F*-paracompact Hausdorff space is both a S*-regular and a WS*-normal space.At last,a discussion about the relations of other paracompactnesses was given.

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Available abstract

F*-paracompactness in L-topological spaces was introduced.It was proved that F*-paracompactness has many good properties,such as that it is L-good extension,hereditary with respect to closed subsets,weakly in homeomorphic invariant property,and that the Cartesian product of a fuzzy compact space and a F*-paracompact space is a F*-paracompact space,as well as that a F*-paracompact Hausdorff space is both a S*-regular and a WS*-normal space.At last,a discussion about the relations of other paracompactnesses was given.

Key concepts: Paracompact space, Hausdorff space, Mathematics, Normal space, Pure mathematics, Cartesian product, Topological space, Regular space

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