Theorems · Theorem · general topology

ContinuousWithinAt.const_smul

∀ {M : Type u_1} {α : Type u_2} {β : Type u_3} [inst : TopologicalSpace α] [inst_1 : SMul M α] [ContinuousConstSMul M α]
  [inst_3 : TopologicalSpace β] {g : β → α} {b : β} {s : Set β},
  ContinuousWithinAt g s b → ∀ (c : M), ContinuousWithinAt (c • g) s b

Defined in

Mathlib.Topology.Algebra.ConstMulAction

Cited by

3 results in Mathlib

Foundations

Depth 60 from the axioms · uses propext, Quot.sound

Assumes

TopologicalSpaceSMulContinuousConstSMulTopologicalSpace