Theorems · Definition · Lie groups

Units.mapContinuousMulEquiv

{M : Type u_1} →
  {N : Type u_2} →
    [inst : TopologicalSpace M] →
      [inst_1 : TopologicalSpace N] → [inst_2 : Monoid M] → [inst_3 : Monoid N] → M ≃ₜ* N → Mˣ ≃ₜ* Nˣ

Any ContinuousMulEquiv induces a ContinuousMulEquiv on units.

Defined in: Mathlib.Topology.Algebra.Group.Units
Cited by: 3 results in Mathlib
Foundations: Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace Monoid Monoid

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Cites7

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
MulEquivproof · cited by 1,142
ContinuousMulEquivstatement and proof · cited by 65
MulEquivClass.toMulEquivproof · cited by 57
Units.mapEquivproof · cited by 16

Cited by3

Results whose statement or proof uses this declaration.

Units.symm_mapContinuousMulEquivstatement · cited by 0
Units.mapContinuousMulEquiv_applystatement and proof · cited by 0
Units.toMulEquiv_mapContinuousMulEquivstatement · cited by 0