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$X \subseteq M(n,\mathbb C) ; |X|>1 ; $ connected/path connected, what about $S:=\{x \in \mathbb C : x $ is an eigenvalue of some matrix in $X\}$?
Let $X \subseteq M(n,\mathbb C)$ be a set with more than one element and $S:=\{x \in \mathbb C : x $ is an eigenvalue of some matrix in $X\}$. I know that if $X$ is compact then so is $S$. My question ...
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