Theorems · Theorem · Lie groups

isOpenMap_vadd_of_sigmaCompact

∀ {G : Type u_1} {X : Type u_2} [inst : TopologicalSpace G] [inst_1 : TopologicalSpace X] [inst_2 : AddGroup G]
  [IsTopologicalAddGroup G] [inst_4 : AddAction G X] [SigmaCompactSpace G] [BaireSpace X] [T2Space X]
  [ContinuousVAdd G X] [AddAction.IsPretransitive G X] (x : X), IsOpenMap fun g => g +ᵥ x

Consider a sigma-compact additive group acting continuously and transitively on a Baire space. Then the orbit map is open. This is a version of the open mapping theorem, valid notably for the action of a sigma-compact locally compact group on a locally compact space.

Defined in

Mathlib.Topology.Algebra.Group.OpenMapping

Cited by

1 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceTopologicalSpaceAddGroupIsTopologicalAddGroupAddActionSigmaCompactSpaceBaireSpaceT2SpaceContinuousVAddAddAction.IsPretransitive