Generalized Open Mapping Theorem for X-Normed Spaces
| Autor: | Angel Barria Comicheo |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
General Mathematics 010102 general mathematics 01 natural sciences Transfinite induction 0103 physical sciences Countable set Uniform boundedness Baire category theorem Closed graph theorem 010307 mathematical physics 0101 mathematics Open mapping theorem (functional analysis) Quotient Mathematics |
| Zdroj: | p-Adic Numbers, Ultrametric Analysis and Applications. 11:135-150 |
| ISSN: | 2070-0474 2070-0466 |
| DOI: | 10.1134/s2070046619020043 |
| Popis: | The theory of X-normed spaces over non-Archimedean valued fields with valuations of higher rank was introduced by H. Ochsenius and W. H. Schikhof in [9] and further developed in [10–12, 16, 17] and [13]. In order to obtain results like the Open Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem, H. Ochsenius and W. H. Schikhof used 1st countability conditions in the value group of the based field. In this article the author develops a new tool to work with transfinite induction simplifying the techniques employed in X-normed spaces, thus accomplishing a Generalized Baire Category Theorem that allows the proof of an Open Mapping Theorem for X-normed spaces without restrictions on the value group of the based field. Additionally, some contributions to the theory of X-normed spaces are presented regarding quotient spaces. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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