Intermediate values and inverse functions on non-Archimedean fields
Continuity or even differentiability of a function on a closed interval of a non-Archimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum, or a unique primitive function on the interval. These problems are due to the total disconnectedness of...
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Hindawi Limited
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202013030 |
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doaj-2edbb112506549ada46bf689b5987fa72020-11-24T22:37:17ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0130316517610.1155/S0161171202013030Intermediate values and inverse functions on non-Archimedean fieldsKhodr Shamseddine0Martin Berz1Department of Mathematics, Michigan State University, East Lansing, MI 48824, USADepartment of Physics and Astronomy, Michigan State University, East Lansing, MI 48824, USAContinuity or even differentiability of a function on a closed interval of a non-Archimedean field are not sufficient for the function to assume all the intermediate values, a maximum, a minimum, or a unique primitive function on the interval. These problems are due to the total disconnectedness of the field in the order topology. In this paper, we show that differentiability (in the topological sense), together with some additional mild conditions, is indeed sufficient to guarantee that the function assumes all intermediate values and has a differentiable inverse function.http://dx.doi.org/10.1155/S0161171202013030 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Khodr Shamseddine Martin Berz |
| spellingShingle |
Khodr Shamseddine Martin Berz Intermediate values and inverse functions on non-Archimedean fields International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Khodr Shamseddine Martin Berz |
| author_sort |
Khodr Shamseddine |
| title |
Intermediate values and inverse functions on non-Archimedean fields |
| title_short |
Intermediate values and inverse functions on non-Archimedean fields |
| title_full |
Intermediate values and inverse functions on non-Archimedean fields |
| title_fullStr |
Intermediate values and inverse functions on non-Archimedean fields |
| title_full_unstemmed |
Intermediate values and inverse functions on non-Archimedean fields |
| title_sort |
intermediate values and inverse functions on non-archimedean fields |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2002-01-01 |
| description |
Continuity or even differentiability of a function on a closed
interval of a non-Archimedean field are not sufficient for the
function to assume all the intermediate values, a maximum, a
minimum, or a unique primitive function on the interval. These
problems are due to the total disconnectedness of the field in
the order topology. In this paper, we show that differentiability
(in the topological sense), together with some additional mild
conditions, is indeed sufficient to guarantee that the function
assumes all intermediate values and has a differentiable inverse
function. |
| url |
http://dx.doi.org/10.1155/S0161171202013030 |
| work_keys_str_mv |
AT khodrshamseddine intermediatevaluesandinversefunctionsonnonarchimedeanfields AT martinberz intermediatevaluesandinversefunctionsonnonarchimedeanfields |
| _version_ |
1725717793294254080 |