非阿基米德域上的中间值定理

Le Matematiche Pub Date : 2013-10-21 DOI:10.4418/2013.68.2.17

L. Corgnier, C. Massaza, P. Valabrega

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引用次数: 3

摘要

本文研究了非阿基米德有序域上幂级数的一般性质，将中间值定理和罗尔定理推广到代数幂级数集合，证明了代数级数在每一个闭区间内都有最大值和最小值。本文还研究了幂级数的收敛性、泰勒绕点展开和零阶的几个性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 interval. The paper also investigates a few properties concerning the convergence of power series, Taylor's expansion around a point and the order of a zero.

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Le Matematiche

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