Theorems · Theorem · general topology
continuous_induced_dom
∀ {α : Type u} {β : Type v} {f : α → β} {t : TopologicalSpace β}, Continuous f- Defined in
- Mathlib.Topology.Order
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- le_rflproof · cited by 1,558
- TopologicalSpace.inducedstatement · cited by 148
- continuous_iff_le_inducedproof · cited by 16
Cited by47
Results whose statement or proof uses this declaration.
- continuous_subtype_valproof · cited by 159
- continuous_applyproof · cited by 120
- RestrictedProduct.continuous_coeproof · cited by 5
- ContinuousMapZero.continuous_precompproof · cited by 4
- MeasureTheory.StronglyAdapted.isStronglyProgressive_of_continuousproof · cited by 4
- MulOpposite.continuous_unopproof · cited by 3
- Units.continuous_embedProductproof · cited by 3
- AddUnits.continuous_embedProductproof · cited by 3
- MeasureTheory.L1.setToL1_nonnegproof · cited by 2
- MeasureTheory.FiniteMeasure.toWeakDualBCNN_continuousproof · cited by 2
- MeasureTheory.ProbabilityMeasure.toFiniteMeasure_continuousproof · cited by 2
- RCLike.nonUnitalContinuousFunctionalCalculusproof · cited by 2