zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Fixed point theorems and Cauchy sequences in fuzzy metric spaces. (English) Zbl 1029.54012
One can find several definitions of the concept of a Cauchy sequence in a fuzzy metric space in the sense of Kramosil and Michalek. This paper presents an example illustrating that definitions given by M. Grabiec [ibid. 27, 385-389 (1989; Zbl 0664.54032)] and R. Vasuki [ibid. 97, 395-397 (1998; Zbl 0960.54005)] are not equivalent to the definition of George and Veeramani. This fact explains in particular why “fixed point type” theorems proved by different authors (see e.g., papers by M. Grabiec, V. Gregori and A. Sapena and R. Vasuki) sometimes have a different “shape”.

54A40Fuzzy topology
54H25Fixed-point and coincidence theorems in topological spaces
54E35Metric spaces, metrizability