Theorems · Theorem · general topology
continuous_iff_le_induced
∀ {α : Type u} {β : Type v} {f : α → β} {t₁ : TopologicalSpace α} {t₂ : TopologicalSpace β},
Continuous f ↔ t₁ ≤ TopologicalSpace.induced f t₂- Defined in
- Mathlib.Topology.Order
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 68 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
- TopologicalSpace.inducedstatement · cited by 148
- continuous_iff_coinduced_leproof · cited by 13
- gc_coinduced_inducedproof · cited by 9
Cited by16
Results whose statement or proof uses this declaration.
- UniformContinuous.continuousproof · cited by 66
- continuous_induced_domproof · cited by 47
- SeparationQuotient.isInducing_mkproof · cited by 7
- continuous_le_domproof · cited by 5
- RestrictedProduct.topologicalSpace_eq_of_principalproof · cited by 5
- FiberPrebundle.continuous_totalSpaceMkproof · cited by 2
- IsModuleTopology.continuous_of_distribMulActionHomₑproof · cited by 2
- continuous_botproof · cited by 2
- Units.isEmbedding_val_mk'proof · cited by 2
- AddUnits.isEmbedding_val_mk'proof · cited by 1
- Subgroup.subgroupOf_isOpenproof · cited by 1
- TestFunction.continuous_iff_continuous_compproof · cited by 0