空间偶与其商空间的未约化同调理论  

Unreduced Homology Theory of Space Pair and Quotient Space

作　　者：唐九奇 刘昌莲 TANG Jiu-qi;LIU Chang-lian(School of Mathematics&Statistics,Guangxi Normal University,Guilin 541000,Guangxi,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541000

出　　处：《红河学院学报》2023年第2期140-142,共3页Journal of Honghe University

摘　　要：在代数拓扑理论中,空间偶与其商空间的未约化同调理论作为一个重要定理.文章主要证明了如下结论:若对于包含映射i:A→X是一个上纤维,那么对于所有的自然数n∈Z^(+),存在一个自然投射p:(X,A)→(X/A,{*})诱导出同构映射射p*:h*(X,A)→≅h_(*)(X/A,{*}).我们的结果依赖于同调函子的切除公理和正合序列公理以及相应的拓扑空间性质.In algebraic topological theory,the unreduced homology theory of a space pair and its quotient space is an important theorem.In this paper,we mainly prove the following conclusions:If the inclusion i:A→X is a cofibration,then the inclusion p:(X,A)→(X/A,{*})induces an isomorphic mapp*:h*(X,A)→≅h_(*)(X/A,{*}).for all n∈Z^(+).Our results depend on the excision axioms and exact sequence axioms and the corresponding properties of topological spaces.

关 键 词：上纤维 切除公理 正合序列 形变收缩核 

分 类 号：O189.2[理学—数学]