On the intermediate value theorem over a non-Archimedean field
The paper investigates general properties of the power series over a non- Archimedean ordered field, extending to the set of algebraic power series the intermediate value theorem and Rolle's theorem and proving that an algebraic series attains its maximum and its minimum in every closed interv...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Università degli Studi di Catania
2013-11-01
|
| Series: | Le Matematiche |
| Subjects: | |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1075 |
| _version_ | 1818318124851658752 |
|---|---|
| author | Luigi Corgnier Carla Massaza Paolo Valabrega |
| author_facet | Luigi Corgnier Carla Massaza Paolo Valabrega |
| author_sort | Luigi Corgnier |
| collection | DOAJ |
| description | The paper investigates general properties of the power series over a non- Archimedean ordered field, extending to the set of algebraic power series the intermediate value theorem and Rolle's theorem and proving that an algebraic series attains its maximum and its minimum in every closed interval.<br /> <br />The paper also investigates a few properties concerning the convergence of power<br />series, Taylor's expansion around a point and the order of a zero. <br /> |
| first_indexed | 2024-12-13T09:48:14Z |
| format | Article |
| id | doaj.art-18f576437eea42c790533933a6a67c3b |
| institution | Directory Open Access Journal |
| issn | 0373-3505 2037-5298 |
| language | English |
| last_indexed | 2024-12-13T09:48:14Z |
| publishDate | 2013-11-01 |
| publisher | Università degli Studi di Catania |
| record_format | Article |
| series | Le Matematiche |
| spelling | doaj.art-18f576437eea42c790533933a6a67c3b2022-12-21T23:51:59ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982013-11-01682227248873On the intermediate value theorem over a non-Archimedean fieldLuigi CorgnierCarla MassazaPaolo ValabregaThe paper investigates general properties of the power series over a non- Archimedean ordered field, extending to the set of algebraic power series the intermediate value theorem and Rolle's theorem and proving that an algebraic series attains its maximum and its minimum in every closed interval.<br /> <br />The paper also investigates a few properties concerning the convergence of power<br />series, Taylor's expansion around a point and the order of a zero. <br />http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1075Ordered fieldsArchimedean propertyPower seriesIntermediate valueExtreme value |
| spellingShingle | Luigi Corgnier Carla Massaza Paolo Valabrega On the intermediate value theorem over a non-Archimedean field Le Matematiche Ordered fields Archimedean property Power series Intermediate value Extreme value |
| title | On the intermediate value theorem over a non-Archimedean field |
| title_full | On the intermediate value theorem over a non-Archimedean field |
| title_fullStr | On the intermediate value theorem over a non-Archimedean field |
| title_full_unstemmed | On the intermediate value theorem over a non-Archimedean field |
| title_short | On the intermediate value theorem over a non-Archimedean field |
| title_sort | on the intermediate value theorem over a non archimedean field |
| topic | Ordered fields Archimedean property Power series Intermediate value Extreme value |
| url | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1075 |
| work_keys_str_mv | AT luigicorgnier ontheintermediatevaluetheoremoveranonarchimedeanfield AT carlamassaza ontheintermediatevaluetheoremoveranonarchimedeanfield AT paolovalabrega ontheintermediatevaluetheoremoveranonarchimedeanfield |