Theorems · Definition · functional analysis
Unitary.openPartialHomeomorph
{A : Type u_1} → [inst : CStarAlgebra A] → OpenPartialHomeomorph ↥(unitary A) ↥(selfAdjoint A)the maps unitary.argSelfAdjoint and selfAdjoint.expUnitary form a partial
homeomorphism between ball (1 : unitary A) 2 and ball (0 : selfAdjoint A) π.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 319 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CStarAlgebra
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddSubgroupstatement · cited by 3,232
- Submonoidstatement · cited by 3,086
- Real.piproof · cited by 1,774
- Metric.ballproof · cited by 735
- OpenPartialHomeomorphstatement · cited by 664
- unitarystatement and proof · cited by 207
- selfAdjointstatement and proof · cited by 135
- CStarAlgebrastatement and proof · cited by 123
- selfAdjoint.expUnitaryproof · cited by 19
- Unitary.argSelfAdjointproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- Unitary.openPartialHomeomorph_applystatement and proof · cited by 0
- Unitary.openPartialHomeomorph_sourcestatement and proof · cited by 0
- Unitary.openPartialHomeomorph_symm_applystatement and proof · cited by 0
- Unitary.openPartialHomeomorph_targetstatement and proof · cited by 0