Theorems · Theorem · Lie groups
Matrix.GeneralLinearGroup.continuous_det
∀ {n : Type u_1} {R : Type u_2} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R]
[inst_3 : TopologicalSpace R] [IsTopologicalRing R], Continuous ⇑Matrix.GeneralLinearGroup.detThe determinant is continuous as a map from the general linear group to the units.
- Defined in
- Mathlib.Topology.Algebra.Group.Matrix
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Unitsstatement · cited by 2,804
- Continuousstatement and proof · cited by 2,592
- Units.valproof · cited by 1,966
- Matrix.GeneralLinearGroupstatement and proof · cited by 556
- IsTopologicalRingstatement and proof · cited by 402
- Matrix.GeneralLinearGroup.detstatement and proof · cited by 58
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.SpecialLinearGroup.isClosedEmbedding_toGLproof · cited by 1