Theorems · Theorem · Lie groups

IsTopologicalGroup.isOpenMap_iff_nhds_one

∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [IsTopologicalGroup G] {H : Type u_1} [inst_3 : Monoid H]
  [inst_4 : TopologicalSpace H] [ContinuousConstSMul H H] {F : Type u_2} [inst_6 : FunLike F G H] [MonoidHomClass F G H]
  {f : F}, IsOpenMap ⇑f ↔ nhds 1 ≤ Filter.map (⇑f) (nhds 1)

Defined in

Mathlib.Topology.Algebra.Group.Basic

Cited by

1 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

TopologicalSpaceGroupIsTopologicalGroupMonoidTopologicalSpaceContinuousConstSMulFunLikeMonoidHomClass