Theorems · Definition · functional analysis
WithLp.uniformEquivProd
(p : ENNReal) → (α : Type u_2) → (β : Type u_3) → [inst : UniformSpace α] → [inst_1 : UniformSpace β] → WithLp p (α × β) ≃ᵤ α × β
WithLp.equiv as a uniform isomorphism.
- Defined in
- Mathlib.Analysis.Normed.Lp.ProdLp
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- UniformSpaceUniformSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- Equivproof · cited by 8,337
- UniformSpacestatement and proof · cited by 2,040
- WithLpstatement and proof · cited by 345
- UniformEquivstatement · cited by 80
- WithLp.equivproof · cited by 8
- WithLp.prod_uniformContinuous_ofLpproof · cited by 0
- WithLp.prod_uniformContinuous_toLpproof · cited by 0
Cited by2
Results whose statement or proof uses this declaration.
- WithLp.toEquiv_uniformEquivProdstatement · cited by 0
- WithLp.toHomeomorph_uniformEquivProdstatement · cited by 0