Theorems · Theorem · general topology
ContinuousMap.idealOfSet_ofIdeal_eq_closure
∀ {X : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] [inst_1 : TopologicalSpace X] [inst_2 : CompactSpace X]
[inst_3 : T2Space X] (I : Ideal C(X, 𝕜)), ContinuousMap.idealOfSet 𝕜 (ContinuousMap.setOfIdeal I) = I.closure- Defined in
- Mathlib.Topology.ContinuousMap.Ideals
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites100
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- Realproof · cited by 25,697
- TopologicalSpacestatement and proof · cited by 24,529
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- NNRealproof · cited by 4,310
- mul_oneproof · cited by 3,885
- LE.le.transproof · cited by 3,151
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousMap.idealOfSet_ofIdeal_isClosedproof · cited by 2
- ContinuousMap.ideal_isMaximal_iffproof · cited by 1