论文标题
横向图的功能空间的拓扑结构
The topological structure of function space of transitive maps
论文作者
论文摘要
令$ c（\ mathbf i）$为$ {\ mathbf i} = [0,1] $的所有连续自动图的集合，并具有均匀收敛的拓扑结构。 c（{\ mathbf i}）$中的地图$ f \如果对于每对非空的开放式设置$ u，$ \ mathbf {i} $中的v $，则称为传递地图，存在一个积极的整数$ n $，因此$ u \ cap f^{ - n}（-n}（-n}（v）\ not = $ n note $ n note $ themt $ themet $ themet $ themt $ themt $ themt $ themt $ themt $ themt $ themt $ themt $ themt $ themt $ themt $ themt $ themt $ themet t。 $ \ Overline {t（\ Mathbf {i}）} $是所有及物地图的集合及其在space $ c（\ mathbf i）$中的关闭。在本文中，我们表明$ t（\ mathbf {i}）$和$ \叠加{
Let $C(\mathbf I)$ be the set of all continuous self-maps from ${\mathbf I}=[0,1]$ with the topology of uniformly convergence. A map $f\in C({\mathbf I})$ is called a transitive map if for every pair of non-empty open sets $U,V$ in $\mathbf{I}$, there exists a positive integer $n$ such that $U\cap f^{-n}(V)\not=\emptyset.$ We note $T(\mathbf{I})$ and $\overline{T(\mathbf{I})}$ to be the sets of all transitive maps and its closure in the space $C(\mathbf I)$. In this paper, we show that $T(\mathbf{I})$ and $\overline{T(\mathbf{I})}$ are homeomorphic to the separable Hilbert space $\ell_2$.
