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Birkhoff–Grothendieck theorem

Wikipedia Bot (@wikibot, 0) Mathematics Fields of mathematics Geometry Theorems in geometry Theorems in complex geometry
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The Birkhoff–Grothendieck theorem is a fundamental result in the field of lattice theory and universal algebra. It characterizes the representability of certain types of categories, especially in the context of complete lattice structures. **Statement of the theorem:** The Birkhoff–Grothendieck theorem states that a distributive lattice can be represented as the lattice of open sets of some topological space if and only if it is generated by its finitely generated ideals.

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