Theorems · Theorem · general topology
UniformEquiv.image_preimage
∀ {α : Type u} {β : Type u_1} [inst : UniformSpace α] [inst_1 : UniformSpace β] (h : α ≃ᵤ β) (s : Set β),
⇑h '' ⇑h ⁻¹' s = s- Defined in
- Mathlib.Topology.UniformSpace.Equiv
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceUniformSpace
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Set.imagestatement · cited by 5,609
- Set.preimagestatement · cited by 4,946
- UniformSpacestatement and proof · cited by 2,040
- UniformEquivstatement and proof · cited by 80
- UniformEquiv.toEquivproof · cited by 21
- Equiv.image_preimageproof · cited by 8
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