Let's note $E=C([0,1],\mathbb{R})$ the Banach space of real continuous funtions from the [0,1] interval with the uniform norm.
Is it possible to show a non linear form on $E$ without using a basis, i.e. without AC?
Non continuous Linear form on $E=C([0,1],\mathbb{R})$ without AC
mathcounterexamples.net
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