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...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2002-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202013030 |
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |