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https://hdl.handle.net/10119/10605
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| Title: | The uniform boundedness theorem and a boundedness principle |
| Authors: | Ishihara, Hajime |
| Keywords: | constructive mathematics
topological vector space
the uniform boundedness theorem
boundedness principle |
| Issue Date: | 2011-12-31 |
| Publisher: | Elsevier |
| Magazine name: | Annals of Pure and Applied Logic |
| Volume: | 163 |
| Number: | 8 |
| Start page: | 1057 |
| End page: | 1061 |
| DOI: | 10.1016/j.apal.2011.12.027 |
| Abstract: | We deal with a form of the uniform boundedness theorem (or the Banach-Steinhaus theorem) for topological vector spaces in Bishop's constructive mathematics, and show that the form is equivalent to the boundedness principle BD-N, and hence holds not only in classical mathematics but also in intuitionistic mathematics and in constructive recursive mathematics.The result is also a result in constructive reverse mathematics. |
| Rights: | NOTICE: This is the author's version of a work accepted for publication by Elsevier. Hajime Ishihara, Annals of Pure and Applied Logic, 163(8), 2011, 1057-1061, http://dx.doi.org/10.1016/j.apal.2011.12.027 |
| URI: | https://hdl.handle.net/10119/10605 |
| Material Type: | author |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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| 17602.pdf | | 162Kb | Adobe PDF | View/Open |
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