Theorems · Theorem · Lie groups
Units.continuous_iff
∀ {M : Type u_1} {X : Type u_3} [inst : TopologicalSpace M] [inst_1 : Monoid M] [inst_2 : TopologicalSpace X]
{f : X → Mˣ}, Continuous f ↔ Continuous (Units.val ∘ f) ∧ Continuous fun x => ↑(f x)⁻¹- Defined in
- Mathlib.Topology.Algebra.Constructions
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Monoidstatement and proof · cited by 3,887
- Unitsstatement and proof · cited by 2,804
- Continuousstatement and proof · cited by 2,592
- Units.valstatement and proof · cited by 1,966
- MulOppositeproof · cited by 1,135
- MulOpposite.opproof · cited by 520
- Homeomorph.symmproof · cited by 365
- Topology.IsInducing.continuous_iffproof · cited by 34
- Homeomorph.isInducingproof · cited by 33
- MulOpposite.opHomeomorphproof · cited by 17
- MulOpposite.opHomeomorph_symm_applyproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Units.continuous_coe_invproof · cited by 4
- Units.continuous_mapproof · cited by 2
- Continuous.units_mapproof · cited by 1