Theorems · Theorem · general topology
ContinuousMap.setOfIdeal_open
∀ {X : Type u_1} {R : Type u_2} [inst : TopologicalSpace X] [inst_1 : Semiring R] [inst_2 : TopologicalSpace R]
[inst_3 : IsTopologicalSemiring R] [T2Space R] (I : Ideal C(X, R)), IsOpen (ContinuousMap.setOfIdeal I)- Defined in
- Mathlib.Topology.ContinuousMap.Ideals
- Cited by
- 1 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.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- Compl.complproof · cited by 2,925
- ContinuousMapstatement and proof · cited by 2,491
- IsOpenstatement and proof · cited by 2,400
- T2Spacestatement and proof · cited by 1,351
- Set.iInterproof · cited by 1,084
- IsTopologicalSemiringstatement and proof · cited by 442
- continuous_constproof · cited by 278
- ContinuousMapClass.map_continuousproof · cited by 119
Cited by2
Results whose statement or proof uses this declaration.
- ContinuousMap.opensOfIdealproof · cited by 3
- ContinuousMap.setOfIdeal_ofSet_eq_interiorproof · cited by 1