Some classical analysis results for continuous definable mappings
Functional Analysis
2021-05-26 v1
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.
Keywords
Cite
@article{arxiv.2105.11652,
title = {Some classical analysis results for continuous definable mappings},
author = {Xuan Duc Ha Truong and Tien Son Pham},
journal= {arXiv preprint arXiv:2105.11652},
year = {2021}
}
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20 pages