关于几类Lindelöf σ-空间
On some classes of Lindelöf Sigma-spaces
摘要：
我们考虑Lindelöf Sigma-空间类的特殊子类，通过对允许可数网络的紧覆盖的元素的权重施加限制而得到：一个空间$X$在$LΣ(\leqκ)$类中，如果它允许权为$κ$的紧子空间的覆盖和覆盖的可数网络。我们只关注$κ\leqω$。在$κ=ω$的情况下，该类包括Tkachuk考虑的度量化纤维空间类和Tkacenko考虑的$P$ -可逼近空间。情况$κ=1$对应于可数网络权重的空间，但即使是情况$κ=2$也会产生一类非平凡的空间。已知类的紧空间，这些类的关系被认为是。证明了不是每个权为$\aleph_1$的Corson紧都在类$LΣ(\leq ω)$中，回答了Tkachuk的一个问题.同时，我们研究了$LΣ(\leqω)$中的某些紧致空间是否有稠密可度量化的子空间，部分回答了Tkacenko的一个问题。其他有趣的结果和例子，我们得出结论的文件与一些开放的问题。
英文摘要：
We consider special subclasses of the class of Lindelöf Sigma-spaces obtained by imposing restrictions on the weight of the elements of compact covers that admit countable networks: A space $X$ is in the class $LΣ(\leqκ)$ if it admits a cover by compact subspaces of weight $κ$ and a countable network for the cover. We restrict our attention to $κ\leqω$. In the case $κ=ω$, the class includes the class of metrizably fibered spaces considered by Tkachuk, and the $P$-approximable spaces considered by Tkacenko. The case $κ=1$ corresponds to the spaces of countable network weight, but even the case $κ=2$ gives rise to a nontrivial class of spaces. The relation of known classes of compact spaces to these classes is considered. It is shown that not every Corson compact of weight $\aleph_1$ is in the class $LΣ(\leq ω)$, answering a question of Tkachuk. As well, we study whether certain compact spaces in $LΣ(\leqω)$ have dense metrizable subspaces, partially answering a question of Tkacenko. Other interesting results and examples are obtained, and we conclude the paper with a number of open questions.
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