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...
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| Format: | Article |
| Language: | English |
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Wiley
1990-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171290000849 |
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| _version_ | 1832563957941927936 |
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| author | Jan Kucera |
| author_facet | Jan Kucera |
| author_sort | Jan Kucera |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-043355c6f11246c08f9eeaef27051b08 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1990-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-043355c6f11246c08f9eeaef27051b082025-02-03T01:12:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251990-01-0113360761010.1155/S0161171290000849Quasi-bounded setsJan Kucera0Department of Mathematics, Washington State University, Pullman 99164-2930, Washington, USAIt 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.http://dx.doi.org/10.1155/S0161171290000849locally convex spaceregular inductive limitbounded and quasi-bounded set. |
| spellingShingle | Jan Kucera Quasi-bounded sets International Journal of Mathematics and Mathematical Sciences locally convex space regular inductive limit bounded and quasi-bounded set. |
| title | Quasi-bounded sets |
| title_full | Quasi-bounded sets |
| title_fullStr | Quasi-bounded sets |
| title_full_unstemmed | Quasi-bounded sets |
| title_short | Quasi-bounded sets |
| title_sort | quasi bounded sets |
| topic | locally convex space regular inductive limit bounded and quasi-bounded set. |
| url | http://dx.doi.org/10.1155/S0161171290000849 |
| work_keys_str_mv | AT jankucera quasiboundedsets |