Theorems · Theorem · Lie groups

MulAction.continuousSMul_compHom

∀ {M : Type u_1} {X : Type u_2} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace X] [inst_2 : Monoid M]
  [inst_3 : MulAction M X] [ContinuousSMul M X] {N : Type u_5} [inst_5 : TopologicalSpace N] [inst_6 : Monoid N]
  {f : N →* M}, Continuous ⇑f → ContinuousSMul N X

If an action is continuous, then composing this action with a continuous homomorphism gives again a continuous action.

Defined in

Mathlib.Topology.Algebra.MulAction

Cited by

1 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceMonoidMulActionContinuousSMulTopologicalSpaceMonoid