I got stuck with the following question. Can you provide me any hint to proceed? Thanks in advance.
From continuity, i know that inverse of any compact set will be closed. However, how am i supposed to show that that set is bounded?
Let $f$, $g$ be non constant monic polynomials with complex coefficients. Then consider the homotopy function, $$ F: [ 0,1 ] \times \mathbb { C } \rightarrow \mathbb { C } , ( t , z ) \mapsto ( 1 - t ) f ( z ) + t g ( z ) $$ Show that $F$ is proper if and only if $\operatorname { deg } ( f ) = \operatorname { deg } ( g )$.