# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
Embedding problem of fuzzy number space. I. (English) Zbl 0757.46066
Summary: Using a theorem of {\it R. Goetschel} and {\it W. Voxman} [ibid. 18, 31- 43 (1986; Zbl 0626.26014)] we can embed fuzzy number space $E\sp 1$ into a concrete Banach space $\overline{C}[0,1]\times\overline{C}[0,1]$. In addition, using a Rådström embedding theorem, {\it M. L. Puri} and {\it D. A. Ralescu} [J. Math. Anal. Appl. 91, 552-558 (1983; Zbl 0528.54009)] embed $E\sp 1$ into a normed space $X$ with $X=C-C$. In fact, $\overline{X}$, the completion of $X$, is isometrically isomorphic to $\overline{C}[0,1]\times\overline{C}[0,1]$.

##### MSC:
 46S40 Fuzzy functional analysis 03E72 Fuzzy set theory 54A40 Fuzzy topology
Full Text:
##### References:
 [1] Bergstrom, H.: Weak convergence of measures. (1982) [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) [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. Proc. 2nd Polish symp. On interval and fuzzy mathematics (1987) [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, 165-169 (1952) · Zbl 0046.33304 [10] Yosida, K.: Functional analysis. (1965) · Zbl 0126.11504