论文标题
绝对关闭的半群
Absolutely closed semigroups
论文作者
论文摘要
令$ \ Mathcal C $为一类拓扑半群。 Semigroup $ x $称为$ $ $ $ \ $ \ MATHCAL C $ - $封闭$，如果对于任何同构$ h：x \ to y $ to y $ to y Mathcal c $ in \ Mathcal c $，则图像$ h [x] $以$ y $关闭。令$ \ Mathsf {t _ {\！1} s} $，$ \ MATHSF {t _ {\！2} s} $，以及$ \ Mathsf {t _ {\！Z} s} $是$ T_1 $，HAUSDORFF，HAUSDORFF，和TYCHONOFF，tyCHONOFF，和TYCHONICATION的类别。 We prove that a commutative semigroup $X$ is absolutely $\mathsf{T_{\!z}S}$-closed if and only if $X$ is absolutely $\mathsf{T_{\!2}S}$-closed if and only if $X$ is chain-finite, bounded, group-finite and Clifford+finite.另一方面，交换性的semigroup $ x $绝对是$ \ mathsf {t _ {\！1} s} $ - 当时关闭，并且仅当$ x $是有限的。另外，对于给定的绝对$ \ MATHCAL C $ C $ c $ x $，我们检测到$ x $中心的绝对$ \ MATHCAL C $ cUMCLASE subsemigroups。
Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called $absolutely$ $\mathcal C$-$closed$ if for any homomorphism $h:X\to Y$ to a topological semigroup $Y\in\mathcal C$, the image $h[X]$ is closed in $Y$. Let $\mathsf{T_{\!1}S}$, $\mathsf{T_{\!2}S}$, and $\mathsf{T_{\!z}S}$ be the classes of $T_1$, Hausdorff, and Tychonoff zero-dimensional topological semigroups, respectively. We prove that a commutative semigroup $X$ is absolutely $\mathsf{T_{\!z}S}$-closed if and only if $X$ is absolutely $\mathsf{T_{\!2}S}$-closed if and only if $X$ is chain-finite, bounded, group-finite and Clifford+finite. On the other hand, a commutative semigroup $X$ is absolutely $\mathsf{T_{\!1}S}$-closed if and only if $X$ is finite. Also, for a given absolutely $\mathcal C$-closed semigroup $X$ we detect absolutely $\mathcal C$-closed subsemigroups in the center of $X$.
