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Exercise 108.62.6 (Dimension). Suppose we have a sober topological space $X$ containing $5$ distinct points $x, y, z, u, v$ having the following specializations

\[ \xymatrix{ x \ar[d] \ar[r] & u & v \ar[l] \ar[dl] \\ y \ar[r] & z } \]

What is the minimal dimension such an $X$ can have? If $X$ is the spectrum of a finite type algebra over a field and $x \leadsto u$ is an immediate specialization, what can you say about the specialization $v \leadsto z$?


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