User:Caliburn/s/fa/Banach-Schauder Theorem/F-Space/Corollary

Theorem
Let $\GF \in \set {\R, \C}$.

Let $\struct {X, d_X}$ be an $F$-space over $\GF$. Let $\struct {Y, d_Y}$ be an $F$-space over $\GF$.

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

Then $T$ is open.