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Let $\mathbb{P}^d_K$ be projective space of dimension $d\geq 1$ over an infinite field $K$. Let $x\in\mathbb{P}^d_K$ with $\dim\overline{\lbrace x\rbrace}=n\leq d-1$. My question: is the set $\lbrace ...

I think the following statement is true. Let $M$ be a real analytic manifold. Let $S \subset M$ be an analytic or semianalytic subset. A point $p \in S$ is called smoothly regular resp. analytically ...