Theorems · Theorem · general topology
continuous_coinduced_dom
∀ {α : Type u} {β : Type v} {γ : Type u_1} {f : α → β} {g : β → γ} {t₁ : TopologicalSpace α} {t₂ : TopologicalSpace γ},
Continuous g ↔ Continuous (g ∘ f)- Defined in
- Mathlib.Topology.Order
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- Continuousstatement · cited by 2,592
- TopologicalSpace.coinducedstatement and proof · cited by 56
- coinduced_composeproof · cited by 6
Cited by13
Results whose statement or proof uses this declaration.
- continuous_sigma_iffproof · cited by 7
- RestrictedProduct.continuous_coeproof · cited by 5
- continuous_sum_domproof · cited by 3
- Continuous.quotient_liftproof · cited by 3
- continuous_stoneCechExtendproof · cited by 2
- continuous_quot_liftproof · cited by 2
- Topology.WithGeneratedByTopology.continuous_from_iffproof · cited by 2
- AddCircle.liftIoc_continuousproof · cited by 1
- Real.tsum_eq_tsum_fourierproof · cited by 1
- AddCircle.liftIco_continuousproof · cited by 1
- continuous_from_compactlyGeneratedproof · cited by 1
- T2Quotient.continuous_liftproof · cited by 0