Theorems · Theorem · manifolds

properSMul_of_isClosedEmbedding

∀ {G : Type u_1} {X : Type u_2} [inst : Group G] [inst_1 : MulAction G X] [inst_2 : TopologicalSpace G]
  [inst_3 : TopologicalSpace X] {H : Type u_3} [inst_4 : Group H] [inst_5 : MulAction H X] [inst_6 : TopologicalSpace H]
  [ProperSMul G X] (f : H →* G), Topology.IsClosedEmbedding ⇑f → (∀ (h : H) (x : X), f h • x = h • x) → ProperSMul H X

If two groups H and G act on a topological space X such that G acts properly and there exists a group homomorphism H → G which is a closed embedding compatible with the actions, then H also acts properly on X.

Defined in

Mathlib.Topology.Algebra.ProperAction.Basic

Cited by

0 results in Mathlib

Foundations

Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionTopologicalSpaceTopologicalSpaceGroupMulActionTopologicalSpaceProperSMul