Theorems · Theorem · general topology

IsUnit.continuousWithinAt_const_smul_iff

∀ {M : Type u_1} {α : Type u_2} {β : Type u_3} [inst : Monoid M] [inst_1 : TopologicalSpace α] [inst_2 : MulAction M α]
  [ContinuousConstSMul M α] [inst_4 : TopologicalSpace β] {f : β → α} {b : β} {c : M} {s : Set β},
  IsUnit c → (ContinuousWithinAt (fun x => c • f x) s b ↔ ContinuousWithinAt f s b)

Defined in

Mathlib.Topology.Algebra.ConstMulAction

Cited by

0 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MonoidTopologicalSpaceMulActionContinuousConstSMulTopologicalSpace