大学数学
大學數學
대학수학
COLLEGE MATHEMATICS
2007年
1期
43-46
,共4页
序列式meso紧%序列式meso紧映射%闭Lindelof映射
序列式meso緊%序列式meso緊映射%閉Lindelof映射
서렬식meso긴%서렬식meso긴영사%폐Lindelof영사
sequential mesocompactness%sequentially-mesocompact mapping%closed Lindelof mapping
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.
證明瞭正則空間中閉Lindelof映射逆保持序列式meso緊性,從而改進瞭Mancuso V J關于正則空間中完備映射逆保持meso緊性這一結果;進一步我們指齣定理條件中原象空間的正則性不可被省略而象空間的正則性可以用原象空間的正規性來替代.
증명료정칙공간중폐Lindelof영사역보지서렬식meso긴성,종이개진료Mancuso V J관우정칙공간중완비영사역보지meso긴성저일결과;진일보아문지출정리조건중원상공간적정칙성불가피성략이상공간적정칙성가이용원상공간적정규성래체대.
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.
