In this paper, by providing some different conditions respect to another works, we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F ： X × X → Pb,cl （...In this paper, by providing some different conditions respect to another works, we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F ： X × X → Pb,cl （X）, on complete metric spaces.展开更多
The space of continuous maps from a topological space X to a topological space Y is denoted by C（X,Y）with the compact-open topology.In this paper we prove that C（X,Y）is an absolute retract if X is a locally compac...The space of continuous maps from a topological space X to a topological space Y is denoted by C（X,Y）with the compact-open topology.In this paper we prove that C（X,Y）is an absolute retract if X is a locally compact separable metric space and Y a convex set in a Banach space.From the above fact we know that C（X,Y）is homomorphic to Hilbert space l<sub>2</sub> if X is a locally compact separable metric space and Y a separable Banach space;in particular,C（R<sup>n</sup>,R<sup>m</sup>） is homomorphic to Hilbert space l<sub>2</sub>.展开更多
文摘In this paper, by providing some different conditions respect to another works, we shall present two results on absolute retractivity of some sets related to some multifunctions of the form F ： X × X → Pb,cl （X）, on complete metric spaces.
基金This research is supported by the Science Foundation of Shanxi Province's Scientific Committee
文摘The space of continuous maps from a topological space X to a topological space Y is denoted by C（X,Y）with the compact-open topology.In this paper we prove that C（X,Y）is an absolute retract if X is a locally compact separable metric space and Y a convex set in a Banach space.From the above fact we know that C（X,Y）is homomorphic to Hilbert space l<sub>2</sub> if X is a locally compact separable metric space and Y a separable Banach space;in particular,C（R<sup>n</sup>,R<sup>m</sup>） is homomorphic to Hilbert space l<sub>2</sub>.
