Let $A$ be the set of square matrix with entries $a_{ij}\in [a,b]$ where $a,b$ is real number. Is $A$ a compact set?
$A$ is bounded set with given a norm however i don't know how to prove the closeness of $A$. Are there any "matrix version sandwich theorem" so that can prove the limit of the given matrix sequence is contains in in $A$? Thank you for any help.