ON LOCAL BOUNDEDNESS OF I-TOPOLOGICAL VECTOR SPACES

Fang, Jin-Xuan; Zhang, Hui

doi:10.22111/ijfs.2012.106

Document Type : Research Paper

Authors

Jin-Xuan Fang ¹
Hui Zhang ²

¹ School of Mathematical Science, Nanjing Normal University, Nan- jing, Jiangsu 210023, P. R. China

² Department of Mathematics, Anhui NormalUniversity, Wuhu, Anhui 241000, P. R. China

https://doi.org/10.22111/ijfs.2012.106

Abstract

The notion of generalized locally bounded $I$-topological vector
spaces is introduced. Some of their important properties are
studied. The relationship between this kind of spaces and the
locally bounded $I$-topological vector spaces introduced by Wu and
Fang [Boundedness and locally bounded fuzzy topological vector
spaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, we
also use the family of generalized fuzzy quasi-norms to characterize
the generalized locally bounded $I$-topological vector spaces, and
give some applications of this characterization.

Keywords

References

[1] J. X. Fang,Local bases with strati ed structure in I-topological vector spaces , Iranian Journal of Fuzzy Systems,7(2) (2010), 83-93.

[2] U. Hohle and S. E. Rodabaugh, eds.Mathematics of fuzzy sets: logic, topology and measure theor, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, 3(1999).

[3] A. K. Katsaras,Fuzzy topological vector spaces I, Fuzzy Sets and Systems, 6 (1981), 85-95.

[4] P. M. Pu and Y. M. Liu,Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76 (1980), 571-599.

[5] S. E. Rodabaugh,Point-set lattice-theoretic topology, Fuzzy Sets and Systems, 40(1991),291-347.

[6] C. X. Wu and J. X. Fang,Rede ne of fuzzy topological vector spaces, Science Exploration,(in Chinese),2(4) (1982), 113-116.

[7] C. X. Wu and J. X. Fang,(QL)-type fuzzy topological vector spaces, Chinese Ann. Math.,(in Chinese),6A(3) (1985), 355􀀀364 or (English summary) 6B(3) (1985), 376.

[8] C. X. Wu and J. X. Fang,Boundedness and locally bounded fuzzy topological vector spaces,Fuzzy Math., (in Chinese),5(4) (1985), 87-94.

[9] C. H. Yan and J. X. Fang,Locally bounded L-topological vector spaces, Information Sciences,159 (2004), 273-281.

[10] H. Zhang and J. X. Fang,On locally convex I-topological vector spaces, Fuzzy Sets and Systems,157 (2006), 1995-2002.

ON LOCAL BOUNDEDNESS OF I-TOPOLOGICAL VECTOR SPACES

References

References

Volume 9, Issue 5 - Serial Number 5November and December 2012Pages 93-104

Volume 9, Issue 5 - Serial Number 5
November and December 2012
Pages 93-104