Theorems · Theorem · ring theory
IsDedekindDomain.isOpen_of_ne_bot
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : TopologicalSpace R] [IsTopologicalRing R] [CompactSpace R] [T2Space R]
[IsDedekindDomain R] {I : Ideal R}, I ≠ ⊥ → IsOpen ↑I- Defined in
- Mathlib.Topology.Algebra.Ring.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- CommRingstatement and proof · cited by 17,173
- SetLike.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- IsOpenstatement and proof · cited by 2,400
- Finset.prodproof · cited by 2,356
- T2Spacestatement and proof · cited by 1,351
- IsDedekindDomainstatement and proof · cited by 668
- CompactSpacestatement and proof · cited by 593
- IsTopologicalRingstatement and proof · cited by 402
- Set.Finite.toFinsetproof · cited by 351
Cited by1
Results whose statement or proof uses this declaration.
- IsDedekindDomain.isOpen_iffproof · cited by 1