Theorems · Theorem · algebraic geometry
PrimeSpectrum.isIdempotentElemEquivClopens_symm_compl
∀ {R : Type u} [inst : CommRing R] (s : TopologicalSpace.Clopens (PrimeSpectrum R)),
PrimeSpectrum.isIdempotentElemEquivClopens.symm sᶜ = ⟨1 - ↑(PrimeSpectrum.isIdempotentElemEquivClopens.symm s), ⋯⟩- Cited by
- 0 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Compl.complstatement · cited by 2,925
- OrderIsostatement · cited by 874
- PrimeSpectrumstatement and proof · cited by 625
- OrderIso.symmstatement and proof · cited by 475
- IsIdempotentElemstatement · cited by 217
- TopologicalSpace.Clopensstatement and proof · cited by 53
- IsIdempotentElem.one_substatement · cited by 20
- PrimeSpectrum.isIdempotentElemEquivClopensstatement and proof · cited by 10
- map_complproof · cited by 2
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