Theorems · Theorem · general topology
ContinuousMap.idealOfSet_closed
∀ {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] (s : Set X), IsClosed ↑(ContinuousMap.idealOfSet R s)- Defined in
- Mathlib.Topology.ContinuousMap.Ideals
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Semiringstatement and proof · cited by 13,802
- SetLike.coestatement and proof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- Idealstatement · cited by 4,748
- Compl.complproof · cited by 2,925
- ContinuousMapstatement and proof · cited by 2,491
- IsClosedstatement and proof · cited by 1,639
- T2Spacestatement and proof · cited by 1,351
- Set.iInterproof · cited by 1,084
Cited by1
Results whose statement or proof uses this declaration.
- ContinuousMap.idealOfSet_ofIdeal_eq_closureproof · cited by 2