环面自映射在拓扑空间中的映射度

Mapping Degree of Self-mapping for Torus in the Topological Space

给出了拓扑空间中环面自映射的可分复迭映射和提升映射的合理定义,对映射度进行了描述.此外,文中界定了环面自映射中的迭代与映射度并研究了环面自映射中的映射度的迭代,得出了对于环面上连续自映射f的映射度的如下结果:若F是f的提升,则1)E*ο Fn=fn ο E*,且Deg(fn)=(Deg(f))n;2)Deg(g ο f)=Deg(f)·Deg(g),(其中g是环面上连续自映射).

In this paper, we give the concepts of covering mapping and upgrade mapping for torus in to-pological space, and use them to score mapping degree.We also study the iteration of mapping degree in the product space for torus in the topological space.And for a continuous mapping f of the torus ,we show：if F is a upgrade of f ,then 1） E＊ .Fn =fn.E＊,且Deg（fn） =（Deg（f））n;2）Deg（g.f） =Deg（f）？ Deg（g）,（g is a continuous mapping） .