光映射和参数Lelek映射的逼近
Approximation by light maps and parametric Lelek maps
摘要：
引入并研究了具有如下逼近性质的可度量化空间类$M$：$M\in AP(n,0)$如果对每个$\e>0$和一个映射$g\colon\I^n\to M$，存在一个0维映射$g'\colon\I^n\to M$与$g$是$\e$ -同伦的.结果表明，该类具有很好的性质。例如，如果$M_i\in AP(n_i,0)$、$i=1,2$，则为$M_1\times M_2\in AP(n_1+n_2,0)$。此外，$M\in AP(n,0)$当且仅当$M$的每个点都有一个局部邻域基$U$与$U\in AP(n,0)$。利用AP（n，0）-空间的性质，推广了Levin和Kato-Matsuhashi关于$n$维Lelek映射剩余集存在性的一些结果.
英文摘要：
The class of metrizable spaces $M$ with the following approximation property is introduced and investigated: $M\in AP(n,0)$ if for every $\e>0$ and a map $g\colon\I^n\to M$ there exists a 0-dimensional map $g'\colon\I^n\to M$ which is $\e$-homotopic to $g$. It is shown that this class has very nice properties. For example, if $M_i\in AP(n_i,0)$, $i=1,2$, then $M_1\times M_2\in AP(n_1+n_2,0)$. Moreover, $M\in AP(n,0)$ if and only if each point of $M$ has a local base of neighborhoods $U$ with $U\in AP(n,0)$. Using the properties of AP(n,0)-spaces, we generalize some results of Levin and Kato-Matsuhashi concerning the existence of residual sets of $n$-dimensional Lelek maps.
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。
