开可分解空间与拓扑半群的紧扩张
Openly factorizable spaces and compact extensions of topological semigroups
摘要：
证明了拓扑半群$S$的半群运算推广到它的斯通-切赫紧化$S$上的连续半群运算，只要$S$是伪紧的可开因式分解空间，这意味着每个到第二可数空间$Y$的映射$f:S\to Y$都可以表示为到第二可数空间$Z$上的开映射$p:X\to Z$和映射$g:Z\to Y$的合成$f=g\circ p$.给出了可开分解空间的谱刻画，并建立了这类空间的一些性质。
英文摘要：
We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its the Stone-Čech compactification $βS$ provided $S$ is a pseudocompact openly factorizable space, which means that each map $f:S\to Y$ to a second countable space $Y$ can be written as the composition $f=g\circ p$ of an open map $p:X\to Z$ onto a second countable space $Z$ and a map $g:Z\to Y$. We present a spectral characterization of openly factorizable spaces and establish some properties of such spaces.
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