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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 579-592, October 2007




SN-COMPACTNESS IN $ L$-TOPOLOGICAL SPACES


BY


ZHEN-GUO XU AND FU-GUI SHI




Abstract. In this paper, the notions of SN-compactness and countable SN-compactness are introduced in $ L$-topological spaces by means of semiclosed $ L$-sets. (Countable) SN-compactness implies (countable) N-compactness, but all the converse fail to be true. The following results are showed: (a) Every $ L$-set with finite support is SN-compact. (b) The intersection of an (a countable) SN-compact $ L$-set and a semiclosed $ L$-set is (countable) SN-compact. (c) The irresolute image of an (a countable) SN-compact $ L$-set is (countable) SN-compact. (d) SN-compactness can be characterized by means of $ \alpha$-nets and $ \alpha$-filters.

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Received September 27, 2005; revised January 7, 2007; March 24, 2007.

AMS Subject Classification. 54A40, 54D35.

Key words. $ L$-topology, semiopen (semiclosed) $ L$-set, N-compactness; SN-compactness; countable SN-compactness.

The project is supported by Scientific Research Common Program of Beijing Municipal Commission of Education (KM200510009009) and The Basic Research Foundation of Beijing Institute of Technology, P.R. China.