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Ben McKay
Ben McKay
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are Are definable sets in an o-minimal expansion of the real field locally analytic?

I have a strong suspicion that yes, but as I am not a specialist in o-minimal structures, I thought that I might have overlooked some corner case.

The precise statement is as follows: let $X \subset \mathbb{R}^n$ be a set definable in an o-minimal structure. Then there exists a point $P \in X$ and an open neighbourhood $O \subset X$ of $P$ such that $O$ is a closed analytic subset of a real analiticanalytic manifold embedded into some open $U \subset \mathbb{R}^n$

are definable sets in o-minimal expansion of the real field locally analytic?

I have a strong suspicion that yes, but as I am not a specialist in o-minimal structures, I thought that I might have overlooked some corner case.

The precise statement is as follows: let $X \subset \mathbb{R}^n$ be a set definable in an o-minimal structure. Then there exists a point $P \in X$ and an open neighbourhood $O \subset X$ of $P$ such that $O$ is a closed analytic subset of a real analitic manifold embedded into some open $U \subset \mathbb{R}^n$

Are definable sets in an o-minimal expansion of the real field locally analytic?

I have a strong suspicion that yes, but as I am not a specialist in o-minimal structures, I thought that I might have overlooked some corner case.

The precise statement is as follows: let $X \subset \mathbb{R}^n$ be a set definable in an o-minimal structure. Then there exists a point $P \in X$ and an open neighbourhood $O \subset X$ of $P$ such that $O$ is a closed analytic subset of a real analytic manifold embedded into some open $U \subset \mathbb{R}^n$

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Dima Sustretov
Dima Sustretov
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are definable sets in o-minimal expansion of the real field locally analytic?

I have a strong suspicion that yes, but as I am not a specialist in o-minimal structures, I thought that I might have overlooked some corner case.

The precise statement is as follows: let $X \subset \mathbb{R}^n$ be a set definable in an o-minimal structure. Then there exists a point $P \in X$ and an open neighbourhood $O \subset X$ of $P$ such that $O$ is a closed analytic subset of a real analitic manifold embedded into some open $U \subset \mathbb{R}^n$