Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Polynomial.isOpenMap_comap_C
∀ {R : Type u_1} [inst : CommRing R], IsOpenMap (PrimeSpectrum.comap Polynomial.C)The morphism C⁺ : Spec R[x] → Spec R is open.
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- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Set.Elemproof · cited by 7,166
- Polynomialstatement and proof · cited by 5,681
- Set.imageproof · cited by 5,609
- Compl.complproof · cited by 2,925
- Set.iUnionproof · cited by 2,483
- IsOpenproof · cited by 2,400
- Polynomial.Cstatement and proof · cited by 1,598
- PrimeSpectrumstatement and proof · cited by 625
- IsOpenMapstatement · cited by 253
- compl_complproof · cited by 229
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