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For questions about frames (=lattices with arbitrary joins and such that finite meets are distributive over those, such as the open sets of a topological set) and locales (the dual category to that of frames, seen as a generalization of topological spaces), as well as about pointfree (“pointless”) topology. This includes questions both of an algebraic nature about frames and of a topological nature about locales.
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Product of topological spaces and product of corresponding locales
Let $\Omega : \mathbf{Top} \to \mathbf{Loc}$ the functor that takes a topological space to its locale of opens.
For a locale morphism $f$, write $f^*$ for the correspoding morphism in $\mathbf{Frm}$, …