论文标题
该间隔的绝对连续同构的产生和通用性
Generation and genericity of the group of absolutely continuous homeomorphisms of the interval
论文作者
论文摘要
我们检查了波兰人组$ h _ {+}^{ac} $的订单保留自我塑料的$ f $的$ \ weft [0,1 \ right] $，$ f $ and $ f $ and $ f $ and $ f^{ - 1} $绝对连续;特别是，我们建立了两个结果。首先，我们证明$ h _ {+}^{ac} $在拓扑上是$ 2 $生成的；实际上，它通常是$ 2 $生成的，即，在h _ {+}^{+}^{ac}^{ac} \ times h _ {+}^{+}^{aC}^{ac} $ in h _ {+}^{aC}^in h _ {+}^{ac} $ in h_ {+}^{aC} $ in y $ \ weft \ weft \ weft \ langle f，g \ right $ d p rang d p y y h _ {+}^{ac}^{ac）其次，我们证明$ h _ {+}^{ac} $允许一个密集的$g_δ$ cogacy类，我们明确表征了其元素。
We examine the Polish group $H_{+}^{AC}$ of order-preserving self-homeomorphisms $f$ of the interval $\left[ 0,1 \right]$ for which both $f$ and $f^{-1}$ are absolutely continuous; in particular, we establish two results. First, we prove that $H_{+}^{AC}$ is topologically $2$-generated; in fact, it is generically $2$-generated, i.e., there is a dense $G_δ$ set of pairs $\left( f,g \right) \in H_{+}^{AC} \times H_{+}^{AC}$ for which $\left\langle f,g \right\rangle$ is dense. Secondly, we prove that $H_{+}^{AC}$ admits a dense $G_δ$ conjugacy class, and we explicitly characterize the elements thereof.
