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arXiv · 2105.11652

Some classical analysis results for continuous definable mappings

Xuan Duc Ha Truong·Tien Son Pham
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Abstract

In this paper, we show that some fundamental results for smooth mappings (e.g., the Brouwer degree formula, the implicit function and inverse function theorems, the mean value theorem, Sard's theorem, Hadamard's global invertibility criteria, Pourciau's surjectivity and openness results) have natural extensions for continuous mappings that are definable in o-minimal structures. The arguments rely on nice properties of definable mappings and sets.

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Xuan Duc Ha Truong, Tien Son Pham. 2021-05-25. Some classical analysis results for continuous definable mappings. https://arxiv.org/abs/2105.11652

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