Theorems · Theorem · algebraic geometry
PrimeSpectrum.isCompact_basicOpen
∀ {R : Type u} [inst : CommSemiring R] (f : R), IsCompact ↑(PrimeSpectrum.basicOpen f)- Cited by
- 3 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coestatement · cited by 8,199
- Algebra.algebraMapproof · cited by 4,706
- TopologicalSpace.Opensstatement · cited by 2,040
- IsCompactstatement and proof · cited by 1,282
- PrimeSpectrumstatement and proof · cited by 625
- Submonoid.powersproof · cited by 408
- Localizationproof · cited by 270
- PrimeSpectrum.basicOpenstatement · cited by 163
- isCompact_rangeproof · cited by 24
- PrimeSpectrum.continuous_comapproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isCompact_isOpen_iffproof · cited by 2
- PrimeSpectrum.exists_constructibleSetData_iffproof · cited by 2
- Polynomial.isCompact_image_comap_of_monicproof · cited by 0