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ON LOCAL BOUNDEDNESS OF I-TOPOLOGICAL VECTOR SPACES | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 8، دوره 9، شماره 5، اسفند 2012، صفحه 93-104 اصل مقاله (378.56 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2012.106 | ||
| نویسندگان | ||
| Jin-Xuan Fang1؛ Hui Zhang2 | ||
| 1School of Mathematical Science, Nanjing Normal University, Nan- jing, Jiangsu 210023, P. R. China | ||
| 2Department of Mathematics, Anhui NormalUniversity, Wuhu, Anhui 241000, P. R. China | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| I-topological vector spaces؛ Generalized locally bounded I-topological vector spaces؛ Family of generalized fuzzy quasi-norms | ||
| مراجع | ||
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[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), 355364 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.
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