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)
On continuous approximations for multifunctions. (English) Zbl 0595.47037
Problems concerning the approximation of convex valued multifunctions by continuous ones are considered. Approximation results of the type obtaind by Gel’man, Cellina, and Hukuhara for Pompeiu-Hausdorff upper semicontinuous multifunctions are shown to hold for some larger classes of multifunctions. Moreover, it is proved that Pompeiu-Hausdorff semicontinuous multifunctions, with convex bounded values, are continuous almost everywhere (in the sense of the Baire category). As an application, an alternative proof is given of Kenderov’s theorem stating that a maximal monotone operator is almost everywhere single-valued.

MSC:
47H05Monotone operators (with respect to duality) and generalizations
58C06Set-valued and function-space valued mappings on manifolds
54C60Set-valued maps (general topology)