3 problems

Let $E\subset\mathbb{R}^n$ be an $\mathscr{A{\\!}R}$-closed set. A function on $E$ is globally subanalytic arc-analytic when it is globally subanalytic and its composition with eve…

Let $X$ be an $\mathscr{A{\!}R}$-closed set in $\mathbb{R}^n$, and let $\mathscr{A}_a(X)$ denote the ring of arc-analytic semialgebraic functions on $X$. Extension conjecture. Ever…

Let $X$ be an $\mathscr{A{\!}R}$-closed set in $\mathbb{R}^n$. Denote by $\mathscr{A}_a(X)$ the ring of arc-analytic semialgebraic functions on $X$, by…