双重映射柱性质的补充

MORE ON THE DOUBLE MAPPING CYLINDER

关于双重映射柱,本文证明了偶对(M(f,λ),X)与(M(f,μ。λ),X)都与(A(f),X)同伦型(其中μ是λ的同伦逆).还给出了从偶对(M(f).X)到(M(f,λ),X)的映射λ的导出映射λ(?),当λ有左同伦逆时,λ有偶对的左同伦逆.后一结果可视为 James Dugundji 的有关定理关于双重映射柱的推广.本文是作者另一篇文章的续篇.

For double mapping cylinder,we prove that the pairs(M(f,λ),X)and (M(f,μμλ),X)are homotopic to the pair(M(f),X),where μ is the homotopy inverse of λ.We give an induced map λ_f from the pair(M(f),X)into(M(f,λ,),X) which has a pair left homotopy inverse when λ has a left homotopy inverse.The result can be viewed as an extension of James Dugundji's theorem in the double mapping cylinder.This paper is a sequel to my another paper.