Banach-Schauder Theorem

Theorem
Let $\struct {X, \norm \cdot_X}$ and $\struct {Y, \norm \cdot_Y}$ be Banach spaces.

Let $T : X \to Y$ be a surjective linear transformation.

Then $T$ is an open mapping.

Proof
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Also known as
This theorem is also known as the open mapping theorem.