关于Alexandroff-Dowker Extension及D_σ-空间的若干结果(英文)

Some Results on Alexandroff-Dowker Extension and D_σ-spaces

证明了空间X是metaLindelf空间(screenable空间)当且仅当X在由具有点可数基(具有σ-不交基)的空间类构成的Alexandroff-Dowker extension中,回答了Arhangel'skii提出的相关问题.另外,通过下面结论对一重要结论进行了推广:可数紧空间是紧空间,如果该空间可以表示为可数多个Dσ-空间的并.

It is shown that a space X is metaLindel（o｜¨）f（screenable） if and only if X is in the Alexandroff-Dowker extension of the class of spaces with a point-countable base（with aσ-disjoint base,respectively）,which gives an answer to one problem raised by Arhangel＇skii. Some results on D_σ-spaces are also obtained.In particular,we prove that a countably compact space X is compact if X is the union of a countable family of D_σ-spaces.