Extensions of 2-point Selections

New Zealand Journal of Mathematics (Online)

S. Garca-Ferreira ; V. Gutev ; T. Nogura

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

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