Theorems · Theorem · Lie groups
Continuous.specialLinearGroup_map
∀ {n : Type u_1} {R : Type u_2} {S : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing R]
[inst_3 : TopologicalSpace R] [inst_4 : CommRing S] [inst_5 : TopologicalSpace S] {f : R →+* S},
Continuous ⇑f → Continuous ⇑(Matrix.SpecialLinearGroup.map f)The topology on SL n R is functorial in R.
- Defined in
- Mathlib.Topology.Algebra.Group.Matrix
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 100 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
- RingHomstatement and proof · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- MonoidHomstatement · cited by 3,629
- Continuousstatement and proof · cited by 2,592
- Continuous.compproof · cited by 371
- Matrix.SpecialLinearGroupstatement · cited by 348
- continuous_idproof · cited by 192
- continuous_subtype_valproof · cited by 159
- Matrix.SpecialLinearGroup.mapstatement · cited by 77
Cited by3
Results whose statement or proof uses this declaration.
- Topology.IsEmbedding.specialLinearGroup_mapproof · cited by 1
- Topology.IsInducing.specialLinearGroup_mapproof · cited by 1
- Matrix.SpecialLinearGroup.continuous_mapGLproof · cited by 0