超空间可缩性

Contractibility of in Hyperspaces

对于一个连续统X,在其上建立超空间Fn(X)={AX:1≤|A|≤n},并在其上建立两种映射φp:Fn(X)→Fn(p,X)和ΨB:Fn(X)→Fn+m(X),给出了φp和ψB是形变收缩映射的充分必要条件以及他们的等价命题.

Let X be a continuum, Author define a hyperspaces Fn（X） ={A belong to X： 1 ≤ ｜A｜ ≤n}, on X. Moreover, consider the mapping φp：Fn（X）→Fn（p,X）和ΨB：Fn（X）→Fn＋m（X）, we find necessary and sufficient conditions under which φp and ΨB are deformation retraction and give some equivalent conditions of them.