Theorems · Theorem · general topology
ContinuousMap.mem_setOfIdeal
∀ {X : Type u_1} {R : Type u_2} [inst : TopologicalSpace X] [inst_1 : Semiring R] [inst_2 : TopologicalSpace R]
[inst_3 : IsTopologicalSemiring R] {I : Ideal C(X, R)} {x : X}, x ∈ ContinuousMap.setOfIdeal I ↔ ∃ f ∈ I, f x ≠ 0- Defined in
- Mathlib.Topology.ContinuousMap.Ideals
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Semiringstatement and proof · cited by 13,802
- Set.ofPredproof · cited by 6,101
- Idealstatement and proof · cited by 4,748
- ContinuousMapstatement and proof · cited by 2,491
- IsTopologicalSemiringstatement and proof · cited by 442
- ContinuousMap.setOfIdealstatement · cited by 12
Cited by4
Results whose statement or proof uses this declaration.
- ContinuousMap.idealOfSet_ofIdeal_eq_closureproof · cited by 2
- ContinuousMap.setOfIdeal_ofSet_eq_interiorproof · cited by 1
- ContinuousMap.setOfTop_eq_univproof · cited by 0
- ContinuousMap.ideal_gcproof · cited by 0