关于不动点集

On Fixed Point Sets

本文证明了:局部连通的完备度量群具有完全不变性质;对于赋范线性空间中关于点x_o为星形的子集S,S的每个含x_o的闭子集为S的不动点集:单纯复合形K的可缩子复形在弱拓扑下为K的不动点集;满的单纯复合形在度量扑拓下具有完全不性性质。

In this paper we obtain the following results:(1)Every locally connected, complete metricc group has the complete invariance property;(2)For a star-shaped set S with respect to the point x_0 of a normed linear space, any closed subset of S containing x_0 is a fixed point set of S;(3)If L is a contractible subcomplex of a simplicial complex K with the weak topology, then L is a fixed point set of K;(4)If K is a full simplicial complex with the metric topology, then K has the complete invariance property.