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Theorems · Theorem · general topology

Continuous.sigma_map

∀ {ι : Type u_5} {κ : Type u_6} {σ : ι → Type u_7} {τ : κ → Type u_8} [inst : (i : ι) → TopologicalSpace (σ i)]
  [inst_1 : (k : κ) → TopologicalSpace (τ k)] {f₁ : ι → κ} {f₂ : (i : ι) → σ i → τ (f₁ i)},
  (∀ (i : ι), Continuous (f₂ i)) → Continuous (Sigma.map f₁ f₂)
Defined in
Mathlib.Topology.Constructions
Cited by
1 results in Mathlib
Foundations
Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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

IsCompactOpenCovered.of_comp · cited by 1IsCompactOpenCovered.of_c…TopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592ContinuousSigma.map · cited by 29Sigma.mapcontinuous_sigma_map · cited by 1continuous_sigma_mapContinuous.sigma_mapCITED BYCITES

Cites4

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Cited by1

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