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I have deleted many irrelevant parts and focused the question considerable, eliminating all the chatter.

edited Jun 11, 2018 at 12:21

Is the image of the map $A \to \bigwedge^k A$ closed over $\mathbb{R}$?

Let $V$ a real vector space of dimension $d$. Let $1<k < d-1$. Consider the map induced by the exterior algebra functor:

$$ \psi:\text{End}(V) \to \text{End}(\bigwedge^kV) \, \, \, \, , \, \, \,\psi(A)=\bigwedge^k A$$

Is the image of $\psi$ closed in the standard topology on the $\text{Hom}$-space?

asked Jun 5, 2018 at 11:10