Theorems · Theorem · general topology
continuous_induced_rng
∀ {α : Type u} {β : Type v} {γ : Type u_1} {f : α → β} {g : γ → α} {t₂ : TopologicalSpace β} {t₁ : TopologicalSpace γ},
Continuous g ↔ Continuous (f ∘ g)- Defined in
- Mathlib.Topology.Order
- Cited by
- 38 results in Mathlib
- Foundations
- Depth 70 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.inducedstatement and proof · cited by 148
- induced_composeproof · cited by 26
Cited by38
Results whose statement or proof uses this declaration.
- Continuous.subtype_mkproof · cited by 51
- MulOpposite.continuous_opproof · cited by 6
- continuous_prodMkproof · cited by 5
- Path.continuous_uncurry_iffproof · cited by 4
- ContinuousMapZero.continuous_precompproof · cited by 4
- WeakBilin.continuous_of_continuous_evalproof · cited by 3
- ContinuousLinearMapWOT.continuous_of_dual_apply_continuousproof · cited by 3
- Continuous.mapPullbackproof · cited by 3
- AddOpposite.continuous_opproof · cited by 3
- continuous_uliftUpproof · cited by 2
- TopologicalSpace.Compacts.continuous_prodproof · cited by 2
- ContMDiff.codRestrict_sphereproof · cited by 2