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In his article "A discrete form of the theorem that each field endomorphismof $\mathbb{R}$ ($\mathbb{Q}_p$) is the identity", Tyszka introduce a logicalproperty which is equivalent to algebraicity in $\mathbb{R}$ and in$\mathbb{Q}_p$. Amazingly, the property is no longer equivalent to algebraicityin $\mathbb{C}$. This article present a similirar property which is equivalentto algebraicity in any field of characteristic zero which is also a Banachspace, and prove a weaker equivalency for fields of positive charcteristic(which are also Banach spaces).

A characterization property on field equivalent to algebraicity on Banach spaces