Theorems · Theorem · general topology
coinduced_le_iff_le_induced
∀ {α : Type u_1} {β : Type u_2} {f : α → β} {tα : TopologicalSpace α} {tβ : TopologicalSpace β},
TopologicalSpace.coinduced f tα ≤ tβ ↔ tα ≤ TopologicalSpace.induced f tβ- Defined in
- Mathlib.Topology.Order
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimageproof · cited by 4,946
- IsOpenproof · cited by 2,400
- TopologicalSpace.inducedstatement and proof · cited by 148
- TopologicalSpace.coinducedstatement and proof · cited by 56
Cited by6
Results whose statement or proof uses this declaration.
- gc_coinduced_inducedproof · cited by 9
- Continuous.le_inducedproof · cited by 8
- induced_generateFrom_eqproof · cited by 5
- pi_generateFrom_eqproof · cited by 2
- prod_generateFrom_generateFrom_eqproof · cited by 0
- prod_eq_generateFromproof · cited by 0