论文标题
双箭的有限力量的自动塑料形态
Autohomeomorphisms of the finite powers of the double arrow
论文作者
论文摘要
令$ \ mathbb {a} $和$ \ mathbb {s} $分别表示Alexandroff和Sorgenfrey线的双重箭头。我们表明，任何同构$ h：^m \ mathbb {a} \ to^m \ mathbb {a} $是本地（除了无处密集集外）单调嵌入$ h_i：j_i \ j_i \ subseteq \ subseteq \ subseteq \ subseteq \ subbb {a} a} \ to \ in \ mathbb \ in} a}（a} a}（a} a}（i}）坐标。我们还证明，对称产品$ \ MATHCAL {F} _M（\ MATHBB {A}）$对于任何$ M \ GEQ 2 $都不是同质的。这部分解决了A.arhangel'skiǐ。相比之下，我们表明对称产品$ \ mathcal {f} _2（\ mathbb {s}）$是同质的。
Let $\mathbb{A}$ and $\mathbb{S}$ denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that any homeomorphism $h:^m\mathbb{A}\to^m\mathbb{A} $ is locally (outside of a nowhere dense set) a product of monotone embeddings $h_i:J_i\subseteq \mathbb{A}\to\mathbb{A} (i\in m)$ followed by a permutation of the coordinates. We also prove that the symmetric products $\mathcal{F}_m(\mathbb{A})$ are not homogeneous for any $m\geq 2$. This partially solves an open question of A. Arhangel'skiǐ. In contrast, we show that symmetric product $\mathcal{F}_2(\mathbb{S})$ is homogeneous.
