On Locally Uniformly Differentiable Functions on a Complete Non-Archimedean Ordered Field Extension of the Real Numbers
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Date
2012-4-17
Authors
Shamseddine, Khodr
Sierens, Todd
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Abstract
We study the properties of locally uniformly differentiable functions on 𝒩, a non-Archimedean field extension of the real numbers that is real closed and Cauchy complete in the topology induced by the order. In particular, we show that locally uniformly differentiable functions are 𝐶1, they include all polynomial functions, and they are closed under addition, multiplication, and composition. Then we formulate and prove a version of the inverse function theorem as well as a local intermediate value theorem for these functions.
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Khodr Shamseddine and Todd Sierens, “On Locally Uniformly Differentiable Functions on a Complete Non-Archimedean Ordered Field Extension of the Real Numbers,” ISRN Mathematical Analysis, vol. 2012, Article ID 387053, 20 pages, 2012. doi:10.5402/2012/387053