# nt.number theory – rank 1 evaluations which are not discrete on finite transcendental extensions of rationals

assume $$K = mathbb {Q} (X_1, dots, X_n)$$ is a purely transcendental extension of rationals on an infinitely indeterminate number. Can anyone give an example of rank $$1$$ evaluation on $$K$$ who fails to be discreet?

If not, is there a theorem which shows that such a rank $$1$$ should the assessment be discreet?