User:Leigh.Samphier/Topology/Spectrum of Locale is Sober Space

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Theorem

Let $\struct{L, \vee, \wedge, \preceq}$ be a locale.

Let $\map {\operatorname{Sp}} L$ denote the spectrum of $L$.

Then:

$\map {\operatorname{Sp}} L$ is a sober space.

Proof

$\blacksquare$