关于纤维到映射的半开性及拟分离映射的半开性
On semi-openness of fiber-onto extensions of minimal semiflows and quasi-separable maps
AI总结：
本文研究了极小流的纤维到扩展及拟分离映射的半开性条件，提出了关于半开映射的结构理论和逆极限技术的应用。
摘要：
本文旨在寻找条件，使得连续满映射ϕ:X→Y及其诱导映射ϕ_*:M¹(X)→M¹(Y)为半开，其中X，Y为紧Hausdorff空间，M¹(X)，M¹(Y)为其Borel概率空间。为此，我们主要通过流的扩展结构理论和逆极限技术证明了以下结果：(1)如果ϕ是极小流的扩展，则ϕ_*为半开。(2)如果ϕ是极小流的拟分离纤维到扩展，则ϕ和ϕ_*均为半开。(3)如果Y是可度量的，则ϕ为半开当且仅当ϕ_*为半开。此外，如果X，Y是左拓扑群，X是Lindelöf拟正则，Y是Baire空间，并且ϕ是局部闭连续满等变映射，则ϕ为半开（这是Pontryagin开放映射定理的推广）。
英文摘要：
The purpose of this paper is to find conditions for a continuous onto map $ϕ\colon X\rightarrow Y$ and its induced map $ϕ_*\colon\mathcal{M}^1(X)\rightarrow\mathcal{M}^1(Y)$ to be semi-open, where $X$, $Y$ are compact Hausdorff spaces and $\mathcal{M}^1(X)$, $\mathcal{M}^1(Y)$ are their Borel probability spaces. For that, we mainly prove the following results by using the structure theory of extensions of semiflows and inverse limit techniques: (1) If $ϕ$ is an extension of minimal flows, then $ϕ_*$ is semi-open. (2) If $ϕ$ is a quasi-separable fiber-onto extension of minimal semiflows, then $ϕ$ and $ϕ_*$ are semi-open. (3) If $Y$ is metrizable, then $ϕ$ is semi-open if and only if $ϕ_*$ is semi-open. In addition, if $X,Y$ are left-topological groups, $X$ is Lindelöf quasi-regular, $Y$ is Baire and if $ϕ$ is a locally closed continuous onto equivariant mapping, then $ϕ$ is semi-open (This is a generalization of Pontryagin's open-mapping theorem).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
