Theorems · Theorem · general topology
ContinuousMap.setOfIdeal_ofSet_of_isOpen
∀ {X : Type u_1} (𝕜 : Type u_2) [inst : RCLike 𝕜] [inst_1 : TopologicalSpace X] [CompactSpace X] [T2Space X]
{s : Set X}, IsOpen s → ContinuousMap.setOfIdeal (ContinuousMap.idealOfSet 𝕜 s) = s- Defined in
- Mathlib.Topology.ContinuousMap.Ideals
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- RCLikestatement and proof · cited by 2,829
- IsOpenstatement and proof · cited by 2,400
- T2Spacestatement and proof · cited by 1,351
- CompactSpacestatement and proof · cited by 593
- IsOpen.interior_eqproof · cited by 58
- ContinuousMap.idealOfSetstatement · cited by 16
- ContinuousMap.setOfIdealstatement · cited by 12
- ContinuousMap.setOfIdeal_ofSet_eq_interiorproof · cited by 1
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