Theorems · Theorem · Lie groups

continuousSMul_iff_stabilizer_isOpen

∀ {M : Type u_1} {X : Type u_2} [inst : TopologicalSpace M] [inst_1 : TopologicalSpace X] [inst_2 : Group M]
  [IsTopologicalGroup M] [inst_4 : MulAction M X] [DiscreteTopology X],
  ContinuousSMul M X ↔ ∀ (x : X), IsOpen ↑(MulAction.stabilizer M x)

A group action of a topological group on a discrete space is continuous if and only if each stabilizer is an open subgroup.

Defined in

Mathlib.Topology.Algebra.MulAction

Cited by

0 results in Mathlib

Foundations

Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceGroupIsTopologicalGroupMulActionDiscreteTopology