ANR上的正规系统、刚性嵌入和不可分吸收集
Normal systems over ANR's, rigid embeddings and nonseparable absorbing sets
摘要：
Besthold和Mogilski [ \textit{Characterizing certain incomplete infinite-dimensional absolute retracts}，Michigan Math. J. \textbf{33}（1986），291- 313]关于ANR的强$Z$ -集和吸收集的大部分结果都推广到不可分的情况。证明了如果ANR $X$是局部同伦稠密可嵌入无穷维Hilbert流形中的，并且对于$X$的每个开非空子集$U$，都有$w(U) = w(X)$（其中“$w$”是拓扑权），则$X$本身是同伦稠密可嵌入Hilbert流形中的.证明了当$X$是AR时，它的弱积$W(X,*) = \{(x_n)_{n=1}^{\infty} \in X^ω:\ x_n = * \textup{for almost all} n\}$同胚于具有$E \cong ΣE$的准Hilbert空间$E$.给出了在这种准希尔伯特空间上建模的流形的一个内在特征.
英文摘要：
Most of results of Bestvina and Mogilski [\textit{Characterizing certain incomplete infinite-dimensional absolute retracts}, Michigan Math. J. \textbf{33} (1986), 291--313] on strong $Z$-sets in ANR's and absorbing sets is generalized to nonseparable case. It is shown that if an ANR $X$ is locally homotopy dense embeddable in infinite-dimensional Hilbert manifolds and $w(U) = w(X)$ (where `$w$' is the topological weight) for each open nonempty subset $U$ of $X$,then $X$ itself is homotopy dense embeddable in a Hilbert manifold. It is also demonstrated that whenever $X$ is an AR, its weak product $W(X,*) = \{(x_n)_{n=1}^{\infty} \in X^ω:\ x_n = * \textup{for almost all} n\}$ is homeomorphic to a pre-Hilbert space $E$ with $E \cong ΣE$. An intrinsic characterization of manifolds modelled on such pre-Hilbert spaces is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
