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## Proyecciones (Antofagasta)

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*Print version* ISSN 0716-0917

### Proyecciones (Antofagasta) vol.27 no.1 Antofagasta May 2008

#### http://dx.doi.org/10.4067/S0716-09172008000100005

Proyecciones Journal of Mathematics

Vol. 27, Nº 1, pp. 81-96, May 2008.

Universidad Católica del Norte

Antofagasta - Chile

O_{R}-CONVERGENCE AND WEAK O_{R}-CONVERGENCE OF NETS AND THEIR APPLICATIONS

**HONGYAN LI ^{1}**

**FUGUI SHI**

^{2}^{1}Shandong Institute of Business and Technolgy, China

^{2}Beijing Institute of Technology, China

Correspondencia a:

**Abstract**

In this paper, the theory of O

_{R}-convergence and weak O

_{R}-convergence of nets is introduced in L-topological spaces by means of neighborhoods and strong neighborhoods of fuzzy points based on Shis O-convergence. It can be used to characterize preclosed sets, preopen sets, δ-closed sets, δ-open sets, near compactness and near S*-compactness.

**Key words :**L-space; neighborhood; strong neighborhood; O

_{R}-convergence; weak O

_{R}-convergence

**Mathematics Subject Classification (2000):**54A40.

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**HONGYAN LI**

School of Mathematics and Information Science,

Shandong Institute of Business and Technolgy,

Beijing 100081,

China

e-mail : __mailto:lihongyan@sdibt.edu.cn__

**FUGUI SHI**

Department of Mathematics,

Beijing Institute of Technology,

Yantai 264005,

China

e-mail : __mailto:fuguishi@bit.edu.cn__

*Received : November 2006. Accepted : March 2007*