On controlled extensions of functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:285

Article

Malesic, J ; Repovs, D ; Semenov, PV

关键词: multivalued mapping;    continuous selection;    controlled extension;    normal space;    soft mapping;   

DOI  :  10.1016/S0022-247X(03)00292-0

来源: Elsevier

【 摘 要 】

For any numerical function E:R-2 -->> R we give sufficient conditions for resolving the controlled extension problem for a closed subset A of a normal space X. Namely, if the functions f:A --> R, g: A --> R and h: X --> R satisfy the equality E(f (a), g(a)) = h(a), for every a is an element of A, then we are interested to find the extensions (f) over cap and (g) over cap of f and g, respectively, such that E((f) over cap (x), (g) over cap (x)) = h(x), for every x is an element of X. We generalize earlier results concerning E(u, v) = u . v by using the techniques of selections of paraconvex-valued LSC mappings and soft single-valued mappings. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free