Weak Darboux property and transitivity of linear mappings on topological vector spaces
| Autor: | V.K. Maslyuchenko, V.V. Nesterenko |
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| Jazyk: | English<br />Ukrainian |
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Karpatsʹkì Matematičnì Publìkacìï, Vol 5, Iss 1, Pp 79-88 (2013) |
| Druh dokumentu: | article |
| ISSN: | 2075-9827 2313-0210 |
| DOI: | 10.15330/cmp.5.1.79-88 |
| Popis: | It is shown that every linear mapping on topological vector spaces always has weak Darboux property, therefore, it is continuous if and only if it is transitive. For finite-dimensional mapping $f$ with values in Hausdorff topological vector space the following conditions are equivalent: (i) $f$ is continuous; (ii) graph of $f$ is closed; (iii) kernel of $f$ is closed; (iv) $f$ is transition map. |
| Databáze: | Directory of Open Access Journals |
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