Theorems · Theorem · general topology
isClosed_coinduced
∀ {α : Type u_1} {β : Type u_2} {t : TopologicalSpace α} {s : Set β} {f : α → β}, IsClosed s ↔ IsClosed (f ⁻¹' s)- Defined in
- Mathlib.Topology.Order
- Cited by
- 5 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimagestatement and proof · cited by 4,946
- Compl.complproof · cited by 2,925
- IsOpenproof · cited by 2,400
- IsClosedstatement · cited by 1,639
- TopologicalSpace.coinducedstatement · cited by 56
- isOpen_coinducedproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- UCompactlyGeneratedSpace.isClosedproof · cited by 2
- SequentialSpace.coinducedproof · cited by 1
- QuotientGroup.t1Space_iffproof · cited by 1
- QuotientAddGroup.t1Space_iffproof · cited by 1
- uCompactlyGeneratedSpace_of_coinducedproof · cited by 1