Let $f: R^n\mapsto R^m$ a linear application.
Is $f$ closed? Why?
Is it open? Why?
2026-02-22 23:26:59.1771802819
How to show that linear applications are closed and open
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The projection $\pi_1: \mathbb{R}^2 \to \mathbb{R}$ is not closed.
Linear maps are open onto their image (open mapping theorem), between Euclidean spaces. Otherwise consider $f(x,y) = (x,0)$ on the plane.