Extensions of 2-point Selections - NZJM

New Zealand Journal of Mathematics

V. Gutev²  T. Nogura¹  S. García-Ferreira³ 

[1] Department of MathematicsFaculty of ScienceEhime UniversityMatsuyama, 790-8577JAPAN$$;School of Mathematical SciencesFaculty of ScienceUniversity of KwaZulu-NatalKing George V AvenueDurban 4041SOUTH AFRICA$$;Instituto de Matemáticas (UNAM)Apartado Postal 61-3Santa Maria58089 MoreliaMichoacánMEXICO$$

关键词: Hyperspace topology;    Vietoris topology;    continuous selection;    selection-regular selection;   

DOI  :  

学科分类：社会科学、人文和艺术（综合）

来源: University of Auckland * Department of Mathematics

【 摘 要 】

We consider a special order-like relation on the subsets of a given space X, which is generated by a continuous selection f for at most 2-point subsets of X. The relation allows to define a "minimal" set of any non-empty compact subset of X, which is then used to construct continuous extensions of f over families of non-empty finite subsets of X. For instance, we show that f can be extended to a continuous selection for at most 3-point subsets if and only if the hyperspace of at most 3-point subsets has a continuous selection. Other possible applications are demonstrated as well.

【 授权许可】

Unknown