= Solution
The <open mapping theorem (functional analysis)> states that a surjective <bounded linear operator> $T:X\to Y$ between <Banach spaces> is an <open map>: $T(U)$ is an <open set> in $Y$ whenever $U$ is an <open set> in $X$. Equivalently, there is $\delta>0$ such that
$$
\boxed{B_Y(0,\delta)\subseteq T(B_X(0,1)),}
$$
where both displayed <balls> are open. In particular, a bijective <bounded linear operator> between <Banach spaces> has a bounded inverse, the <bounded inverse theorem>.
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