Theorems · Theorem · general topology
continuous_iff_coinduced_le
∀ {α : Type u} {β : Type v} {f : α → β} {t₁ : TopologicalSpace α} {t₂ : TopologicalSpace β},
Continuous f ↔ TopologicalSpace.coinduced f t₁ ≤ t₂- Defined in
- Mathlib.Topology.Order
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 65 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 · cited by 56
- continuous_defproof · cited by 21
Cited by13
Results whose statement or proof uses this declaration.
- continuous_coinduced_rngproof · cited by 19
- continuous_iff_le_inducedproof · cited by 16
- Topology.IsQuotientMap.continuous_iffproof · cited by 10
- continuous_generateFrom_iffproof · cited by 7
- continuous_le_rngproof · cited by 3
- IsModuleTopology.isQuotientMap_of_surjectiveₛₗproof · cited by 3
- continuous_sSup_rngproof · cited by 1
- AddGroupTopology.coinduced_continuousproof · cited by 0
- TestFunction.continuous_ofSupportedInproof · cited by 0
- GroupTopology.coinduced_continuousproof · cited by 0
- coinduced_nhdsAdjointproof · cited by 0
- RingTopology.coinduced_continuousproof · cited by 0