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• ### Failure of the Hahn-Banach in ℂₚ

The Hahn-Banach is known to be a crucial tool in functional analysis. The following are lecture notes written a while ago for my functional analysis course on the failure of Hahn-Banach in the $p$-adic completion of $\bar{\mathbb{Q}}_p$ (denoted by $\mathbb{C}_p$). For those who are well-versed in the basics of $\mathbb{Q}_p$, I would recommend skipping to…