If $f_n$ is a sequence of smooth orientation preserning mappings of degree one between open annuli $A(1,r):=\{x: 1< |x| < r \}$ and $A(1,r_n)$, $r>1$ and $r_n>1$, on the Euclidean space $\mathbf{R}^d$, converging (in compacts of $A(1,r)$ together with the derivatives) to a smooth mapping $f$. What can be said about the degree of $f$?

If $f_n$ is a sequence of smooth orientation preserning mappings of degree one between open annuli $A(1,r):=\{x: 1< |x| < r \}$ and $A(1,r_n)$, $r>1$ and $r_n>1$, on the Euclidean space $\mathbf{R}^d$, converging (in compacts of $A(1,r)$ together with the derivatives) to a smooth mapping $f$. What can be said about the degree of $f$?

Of course all the mappings $f_n$ are sirjective and for einstance map the inner (outer) boundary onto inner (outer) boundary

If $f_n$ is a sequence of smooth orientation preserning mappings of degree one between annuli $A(1,r)$ and $A(1,r_n)$, $r>1$ and $r_n>1$, on the Euclidean space $\mathbf{R}^d$, converging (in compacts of $A(1,r)$ together with the derivatives) to a smooth mapping $f$. What can be said about the degree of $f$?

If $f_n$ is a sequence of smooth orientation preserning mappings of degree one between open annuli $A(1,r):=\{x: 1< |x| < r \}$ and $A(1,r_n)$, $r>1$ and $r_n>1$, on the Euclidean space $\mathbf{R}^d$, converging (in compacts of $A(1,r)$ together with the derivatives) to a smooth mapping $f$. What can be said about the degree of $f$?