Document Type: Research Paper

Author

Department of Mathematics, Qaemshhar Branch, Islamic Azad University, Qaemshahr, Iran.

Abstract

The present paper introduces the notion of the complete fuzzy norm on a linear space. And, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. Some characterizations of their properties are obtained.

Keywords

[1] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear space, J. Fuzzy Math., 11 (2003) No. 3, 687-705.

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

[3] A. K. Katsaras, Fuzzy topological vector space II, Fuzzy sets and systems., 12 (1984) 143- 154.

[4] A. K. Katsaras, Fuzzy vector spaces and fuzzy topological vector spaces, J. Math. Anal. Appl., 58 (1977) 135-146.

[5] S. V. Krishna and K. K. M. Sarma, Fuzzy topological vector spaces – topological generation and normability, Fuzzy sets and systems., 41 (1991) 89-99.

[6] S. V. Krishna and K. K. M. Sarma, Fuzzy continuity of linear maps on vector spaces, Fuzzy sets and systems., 45 (1992) 341-354.

[7] S. V. Krishna and K. K. M. Sarma, Seperation of fuzzy normed linear spaces, Fuzzy sets and systems., 63 (1994) 207-217.

[8] R. Larsen, Functional analysis, Marcel Dekker, Inc. New york, 1973.

[9] G. S. Rhie, B. M. Choi and D. S. Kim, On the completeness of fuzzy normed linear spaces, Math. Japonica., 45 (1997) no. 1, 33-37.

[10] R. H. Warren, Neighborhoods bases and continuity in fuzzy topological spaces, Rocky Mountain J. Math., 8 (1978) 459-470.