Galois Connections and Nullstellensatzen

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(The idea for this post is due to this tweet by @sarah_zrf) Hilbert’s Nullstellensatz Consider the ring of complex polynomials in \(n\) variables, \(\mathbb{C}[x_1,x_2,\dots x_n]\). The elements of thing ring can be viewed as functions \(\mathbb{C}^n \to \mathbb{C}\). Given a polynomial \(f\), we can think of it as an equation in \(n\) variables - a solution to the equation is a tuple…

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