A Fixed Point Theorem and Equivariant Points for Set-valued Mappings
A Fixed Point Theorem and Equivariant Points for Set-valued Mappings
复制标题
集值映射的不动点定理和等变点
DOI：
10.2977/prims/1249478966
复制
发表时间：
2009
影响因子：
1.2
通讯作者：
Yoshimi Shitanda
中科院分区：
文献类型：
--
作者：
Yoshimi Shitanda
证明了Vietoris映象与紧映象的重合定理，证明了含有上半连续非循环映象的容许映象的Lefschetz不动点定理。当源空间是具有自由对合的仿紧Hausdorff空间，目标空间是具有对合的闭拓扑流形时，在一定条件下证明了这类容许映象的等变点的存在性。当源空间是具有有限覆盖维度的Poincare空间时，确定等变点集合的覆盖维度。
We give a proof of a coincidence theorem for a Vietoris mapping and a compact mapping and prove the Lefschetz fixed point theorem for the class of admissible mappings which contains upper semi-continuous acyclic mappings. When a source space is a paracompact Hausdorff space with a free involution and a target space is a closed topological manifold with an involution, the existence of equivariant points is proved for the class of admissible mappings under some conditions. When a source space is a Poincare space with a finite covering dimension, the covering dimension of the set of equivariant points is determined.