Theorems · Theorem · Lie groups

IsTopologicalAddGroup.isOpenMap_iff_nhds_zero

∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : AddGroup G] [IsTopologicalAddGroup G] {H : Type u_1}
  [inst_3 : AddMonoid H] [inst_4 : TopologicalSpace H] [ContinuousConstVAdd H H] {F : Type u_2} [inst_6 : FunLike F G H]
  [AddMonoidHomClass F G H] {f : F}, IsOpenMap ⇑f ↔ nhds 0 ≤ Filter.map (⇑f) (nhds 0)

Defined in

Mathlib.Topology.Algebra.Group.Basic

Cited by

0 results in Mathlib

Foundations

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

Assumes

TopologicalSpaceAddGroupIsTopologicalAddGroupAddMonoidTopologicalSpaceContinuousConstVAddFunLikeAddMonoidHomClass