Quasi-bounded sets
It is proved in [1] & [2] that a set bounded in an inductive limit E=indlim En of Fréchet spaces is also bounded in some En iff E is fast complete. In the case of arbitrary locally convex spaces En every bounded set in a fast complete indlim En is quasi-bounded in some En, though it may not be b...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1990-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171290000849 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | It is proved in [1] & [2] that a set bounded in an inductive limit E=indlim En of Fréchet spaces is also bounded in some En iff E is fast complete. In the case of arbitrary locally convex spaces En every bounded set in a fast complete indlim En is quasi-bounded in some En, though it may not be bounded or even contained in any En. Every bounded set is quasi-bounded. In a Fréchet space every quasi-bounded set is also bounded. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |