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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 691-706, October 2007




$ O_\theta$-CONVERGENCE AND WEAK $ O_\theta$-CONVERGENCE

OF NETS AND THEIR APPLICATIONS


BY


HONG-YAN LI AND FU-GUI SHI




Abstract. In this paper, the theory of $ O_\theta$-convergence and weak $ O_\theta$-convergence of nets is introduced in $ L$-spaces by means of neighborhoods and strong neighborhoods of fuzzy points based on Shi's $ O$-convergence. It can be used to characterize preclosed sets, preopen sets, $ \theta$-closed sets, $ \theta$-open sets, almost $ F$-compactness and almost $ S^*$-compactness.

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Received May 17, 2006; revised January 29, 2007.

AMS Subject Classification. 54A40.

Key words. $ L$-space; neighborhood, strong neighborhood, $ O_\theta$-convergence, weak $ O_\theta$-convergence.