In Rudin's Functional Analysis (in theorem 3.4), he says:(adsbygoogle = window.adsbygoogle || []).push({});

"every nonconstant linear functional on X is an open mapping". X is topological vector space.

This seems like a strengthening of the open mapping theorem, which requires X to be an F-Space, and that the linear functional to be continuous.

Indeed, it seems like a discontinuous linear functional from R to R as described in Gelbaum for instance isn't open.

What am I missing?

thanks

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# Linear functional clarification (from rudin)

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