丘京辉.拟速完备性与网状空间的诱导极限(英文)[J].数学研究及应用,1998,18(1):55~59 |
拟速完备性与网状空间的诱导极限(英文) |
Quasi Fast Completeness and Inductive Limits of Webbed Spaces |
投稿时间:1995-05-28 |
DOI:10.3770/j.issn:1000-341X.1998.01.009 |
中文关键词: |
英文关键词:locally convex spaces inductive limits webbed spaces. |
基金项目: |
|
摘要点击次数: 2264 |
全文下载次数: 1056 |
中文摘要: |
设(E,ζ)=indlim(En,ζn)为局部凸空间的诱导极限.称(DST)成立若(E,ζ)中每个有界集含于且有界于某(En,ζn).引进一种弱于速完备性的性质,叫做拟速完备性,并证明了对于严格网状空间的诱导极限,拟速完备性蕴涵(DST).利用DeWilde的理论,也给出了关于(DST)的其他条件.这些结果改进了已有的有关结论 |
英文摘要: |
Let (E,ζ)= indlim (En ,ζn) be an inductive limit of locally convex spaces. We say that ( DST ) holds if each bounded set in (E,ζ) is contained and bounded in some (En,ζn). We introduce a property which is weaker than fast completeness, quasi-fast completeness, and prove that for inductive limits of strictly webbed spaces, quasi-fast completeness implies that ( DST ). By using De Wilde’s theory on webbed spaces,we also give some other conditions for (DST). These results improve relevant earlier results |
查看全文 查看/发表评论 下载PDF阅读器 |
|
|
|