论文标题
在连续的自图的空间中，非题材是茂密的
The non-iterates are dense in the space of continuous self-maps
论文作者
论文摘要
在本文中，我们开发了一种工具来识别没有任何顺序迭代根的功能。 Using this, we prove that when $X$ is $[0,1]^m$, $\mathbb{R}^m$ or $S^1$, every non-empty open set of the space $\mathcal{C}(X)$ of continuous self-maps on $X$ endowed with the compact-open topology contains a map that does not have even discontinuous iterative roots of order $n\ge 2$.特别地，这证明了$ \ {f^n：f \ in \ Mathcal {c}（x）〜\ text {and} 〜n \ ge 2 \} $的补充，非介质的集合，在这些$ x $中是$ \ mathcal {c}（x）$。
In this paper we develop a tool to identify functions which have no iterative roots of any order. Using this, we prove that when $X$ is $[0,1]^m$, $\mathbb{R}^m$ or $S^1$, every non-empty open set of the space $\mathcal{C}(X)$ of continuous self-maps on $X$ endowed with the compact-open topology contains a map that does not have even discontinuous iterative roots of order $n\ge 2$. This, in particular, proves that the complement of $\{f^n: f\in \mathcal{C}(X)~\text{and}~n\ge 2\}$, the set of non-iterates, is dense in $\mathcal{C}(X)$ for these $X$.
