Academic Journal
A revised closed graph theorem for quasi-Suslin spaces
| العنوان: | A revised closed graph theorem for quasi-Suslin spaces |
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| المؤلفون: | Ferrando, J. C., Kąkol, J., Lopez Pellicer, M. |
| بيانات النشر: | Institute of Mathematics, Academy of Sciences of the Czech Republic Matematický ústav AV ČR |
| سنة النشر: | 2009 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:$K$-analytic space, keyword:web space, keyword:quasi-Suslin space, msc:46A03, msc:46A30, msc:54C05, msc:54C14, msc:54D08 |
| الوصف: | summary:Some results about the continuity of special linear maps between $F$-spaces recently obtained by Drewnowski have motivated us to revise a closed graph theorem for quasi-Suslin spaces due to Valdivia. We extend Valdivia's theorem by showing that a linear map with closed graph from a Baire tvs into a tvs admitting a relatively countably compact resolution is continuous. This also applies to extend a result of De Wilde and Sunyach. A topological space $X$ is said to have a (relatively countably) compact resolution if $X$ admits a covering $\{A_{\alpha }\:\alpha \in \Bbb N^{\Bbb N}\}$ consisting of (relatively countably) compact sets such that $A_{\alpha }\subseteq A_{\beta }$ for $\alpha \leq \beta $. Some applications and two open questions are provided. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0011-4642 1572-9141 |
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| الاتاحة: | http://hdl.handle.net/10338.dmlcz/140541 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.C233DDA9 |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 00114642 15729141 |
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