无限维拓扑中的AR和ANR

About AR and ANR in Infinite-Dimensional Topology

无限维拓扑学是拓扑学的一个新的领域,文章介绍了有关ANR和AR相关的性质,并且给出以下几个命题:1)ANR的有限积是ANR.2)每一个可缩空间是道路连通的.3)X上的每一个单位分解是可数集.4)X={0,1}是ANR,不是AR.5)X是AR X是ANR.6)AR的收缩核是AR,ANR的邻域的收缩核是ANR.并且给予了证明.

Infinite-dimensional topology is a new domain of topology. ANR and AR are introduced. At the same time ,some propositions about ANR and AR are proved. For example： 1） the product of finitely many ANR＇s is an ANR. 2）every contractible space is path-connected. 3） each partition of unity on is countable. 4） the space X= {0,1} is an ANR but is not an AR. 5） every AR is an ANR 6）every retract of an AR is AR,and every neighborhood retract of an ANR is again an ANR.