序列式MESO紧空间的闭Lindelof逆象(英文)

On Closed Lindelof Inverse Images of Sequentially Mesocompact Spaces

证明了正则空间中闭Lindelof映射逆保持序列式meso紧性,从而改进了Mancuso V J关于正则空间中完备映射逆保持meso紧性这一结果;进一步我们指出定理条件中原象空间的正则性不可被省略而象空间的正则性可以用原象空间的正规性来替代.

We prove that closed Lindelof mappings with regular domains and images inversely preserve sequential mesocompactness, which improves the same result of Mancuso V J about perfect mappings. Also we proved that the regularity of domains cannot be omitted and the regularity of images can be replaced by the normality of domains.