A note on D-spaces and infinite unions

作者：Peng Liang Xue^*

来源：Topology and Its Applications, 2007, 154(11): 2223-2227.

DOI：10.1016/j.topol.2007.01.020

• D-space
• k-network
• sequential space
• compact

It is shown that if X is a countably compact space that is the union of a countable family of D-spaces, then X is compact. This gives a positive answer to Arhangel'skii's problem [A.V. Arhangel'skii, D-spaces and finite unions, Proc. Amer. Math. Soc. 132 (7) (2004) 2163-2170]. In this note, we also obtain a result that if a regular space X is sequential and has a point-countable k-network, then X is a D-space.

• 出版日期2007-6-1
• 单位北京工业大学