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Theorems · Theorem · general topology

continuousAt_pi

∀ {X : Type u} {ι : Type u_5} {A : ι → Type u_6} [inst : TopologicalSpace X] [T : (i : ι) → TopologicalSpace (A i)]
  {f : X → (i : ι) → A i} {x : X}, ContinuousAt f x ↔ ∀ (i : ι), ContinuousAt (fun y => f y i) x
Defined in
Mathlib.Topology.Constructions
Cited by
2 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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ContinuousAt.piMap · cited by 0ContinuousAt.piMapcontinuousAt_pi' · cited by 0continuousAt_pi'TopologicalSpace · cited by 24529TopologicalSpaceContinuousAt · cited by 697ContinuousAttendsto_pi_nhds · cited by 58tendsto_pi_nhdscontinuousAt_piCITED BYCITES

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Cited by2

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