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Preprint Number 1980
1980. Siegfried Van Hille Mild parametrizations of power-subanalytic sets E-mail: Submission date: 11 May 2021 Abstract: We obtain two uniform parametrization theorems for families of bounded sets definable in ℝ_{an}^ℝ. Let X = { X_t ⊆ (0,1)^n | t in T } be a definable family of sets X_t of dimension at most m. Firstly, X_t admits a C^r-parametrization consisting of cr^m maps for some positive constant c = c(X), which is uniform in t. Secondly, X_t admits a C-mild parametrization for any C>1, which is also uniform in t. Mathematics Subject Classification: 03C98, 14P15 (Primary), 11D99 (Secondary) Keywords and phrases: |

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