Theorems · Theorem · general topology
ULift.isOpen_iff
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set (ULift.{v, u} X)}, IsOpen s ↔ IsOpen (ULift.up ⁻¹' s)- Defined in
- Mathlib.Topology.Constructions
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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
- IsOpenstatement and proof · cited by 2,400
- Equiv.uliftproof · cited by 115
- isOpen_coinducedproof · cited by 12
- Equiv.ulift_applyproof · cited by 2
- Equiv.coinduced_symmproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- ULift.isClosed_iffproof · cited by 0