Wu, Congxin; Ma, Ming Embedding problem of fuzzy number space. I. (English) Zbl 0757.46066 Fuzzy Sets Syst. 44, No. 1, 33-38 (1991). Summary: Using a theorem of R. Goetschel and W. Voxman [ibid. 18, 31- 43 (1986; Zbl 0626.26014)] we can embed fuzzy number space \(E^ 1\) into a concrete Banach space \(\overline{C}[0,1]\times\overline{C}[0,1]\). In addition, using a Rådström embedding theorem, M. L. Puri and D. A. Ralescu [J. Math. Anal. Appl. 91, 552-558 (1983; Zbl 0528.54009)] embed \(E^ 1\) into a normed space \(X\) with \(X=C-C\). In fact, \(\overline{X}\), the completion of \(X\), is isometrically isomorphic to \(\overline{C}[0,1]\times\overline{C}[0,1]\). Cited in 6 ReviewsCited in 102 Documents MSC: 46S40 Fuzzy functional analysis 03E72 Theory of fuzzy sets, etc. 54A40 Fuzzy topology Keywords:isometrical isomorphism; fuzzy number space; concrete Banach space; Rådström embedding theorem Citations:Zbl 0626.26014; Zbl 0528.54009 PDF BibTeX XML Cite \textit{C. Wu} and \textit{M. Ma}, Fuzzy Sets Syst. 44, No. 1, 33--38 (1991; Zbl 0757.46066) Full Text: DOI References: [1] Bergstrom, H., Weak Convergence of Measures (1982), Academic Press: Academic Press New York · Zbl 0538.28003 [2] Goetschel, R.; Voxman, W., Elementary fuzzy calculus, Fuzzy Sets and Systems, 18, 31-43 (1986) · Zbl 0626.26014 [3] Natanson, N., Theory of Real Variables (1950), Soviet Academic Press: Soviet Academic Press Moscow, (in Russian) [4] Kaleva, O., Fuzzy differential equations, Fuzzy Sets and Systems, 24, 301-317 (1987) · Zbl 0646.34019 [5] Kaleva, O., The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems, 35, 389-396 (1990) · Zbl 0696.34005 [6] Marłoka, M., On fuzzy integrals, (Albrycht, J.; Wisnieski, H., Proc. 2nd Polish Symp. on Interval and Fuzzy Mathematics (1987), Politechnika Poznansk: Politechnika Poznansk Poznan) [7] Puri, M. L.; Ralescu, D. A., Differentials for fuzzy functions, J. Math. Anal. Appl., 91, 552-558 (1983) · Zbl 0528.54009 [8] Puri, M. L.; Ralescu, D. A., Fuzzy random variables, J. Math. Anal. Appl., 114, 409-422 (1986) · Zbl 0592.60004 [9] Rådström, H., An embedding theorem for spaces of convex sets, (Proc. Amer. Math. Soc., 3 (1952)), 165-169 · Zbl 0046.33304 [10] Yosida, K., Functional Analysis (1965), Springer-Verlag: Springer-Verlag Berlin · Zbl 0126.11504 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.