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ContinuousAt.pow

∀ {M : Type u_3} {X : Type u_5} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace M] [inst_2 : Monoid M]
  [ContinuousMul M] {f : X → M} {x : X}, ContinuousAt f x → ∀ (n : ℕ), ContinuousAt (f ^ n) x
Defined in
Mathlib.Topology.Algebra.Monoid
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpaceMonoidContinuousMul
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousAt.fun_pow · cited by 7ContinuousAt.fun_powTopologicalSpace · cited by 24529TopologicalSpaceMonoid · cited by 3887MonoidContinuousAt · cited by 697ContinuousAtContinuousMul · cited by 343ContinuousMulFilter.Tendsto.pow · cited by 16Tendsto.powContinuousAt.powCITED BYCITES

Cites5

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Cited by1

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