Locally constant functions in C-minimal structures

Pablo Cubides Kovacsics

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arXiv · 1410.3144

Locally constant functions in C-minimal structures

Pablo Cubides Kovacsics

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Abstract

Let $M$ be a $C$-minimal structure and $T$ its canonical tree (which corresponds in an ultrametric space to the set of closed balls with radius different than $\infty$ ordered by inclusion). We present a description of definable locally constant functions $f:M\rightarrow T$ in $C$-minimal structures having a canonical tree with infinitely many branches at each node and densely ordered branches. This provides both a description of definable subsets of $T$ in one variable and analogues of known results in algebraically closed valued fields.

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BibTeX RIS

Pablo Cubides Kovacsics. 2014-10-12. Locally constant functions in C-minimal structures. https://arxiv.org/abs/1410.3144

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