Theorems · Theorem · general topology
boundedSpace_subtype_iff
∀ {α : Type u_1} [inst : Bornology α] {p : α → Prop}, BoundedSpace (Subtype p) ↔ Bornology.IsBounded {x | p x}- Defined in
- Mathlib.Topology.Bornology.Constructions
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Bornology
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Set.ofPredstatement and proof · cited by 6,101
- Bornology.IsBoundedstatement and proof · cited by 293
- Bornologystatement and proof · cited by 188
- Subtype.range_coe_subtypeproof · cited by 170
- BoundedSpacestatement · cited by 26
- boundedSpace_induced_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- boundedSpace_val_set_iffproof · cited by 2
- Bornology.IsBounded.boundedSpace_subtypeproof · cited by 0