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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 [latex]p[/latex]-adic completion of [latex]\bar{\mathbb{Q}}_p[/latex] (denoted by [latex]\mathbb{C}_p[/latex]). For those who are well-versed in the basics of [latex]\mathbb{Q}_p[/latex], I would recommend skipping to…