The study for covering properties of topological spaces and their products in terms of elementary submodels

这本书的编辑题为“最近的进展一般拓扑III”让我写一份调查有关“覆盖性质”与P. Szeptycki。在此基础上，我们讨论了初等子模型的一些应用，并将初等子模型的研究与具有单调正规因子的乘积的覆盖性质和正规性的研究联系起来。这些研究有一个相似的方面，在这个意义上，证明是由集理论的方法，但结论是完全由一般拓扑表示。2011年和2012年发表了两篇关于这一主题的论文。目前，由于得到了Kemoto Nobuyuki和Yasushi Hirata的合作，这一研究得到了很大的发展。

The editor of the book titled "Recent Progress in General Topology III" asked me to write a survey concerning "Covering properties" with P. Szeptycki. We have taken up some applications of elementary submodels in it. Then the study of elementary submodels has been connected to that of covering properties and normality of the products with a monotonically normal factor. These studies have a similar aspect in the sense that the proofs are done by set-theoretic methods but the conclusions are completely expressed by general topology. Two papers have been published in 2011 and 2012 for this subject. In the present, getting the corporation with Nobuyuki Kemoto and Yasushi Hirata, this study has been greatly developed.