Theorems · Theorem · general topology
IsClosed.relPreimage_of_isCompact
∀ {α : Type ua} {β : Type ub} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {s : SetRel α β},
IsClosed s → ∀ {t : Set β}, IsCompact t → IsClosed (s.preimage t)- Defined in
- Mathlib.Topology.UniformSpace.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- nhdsproof · cited by 5,554
- Filter.Eventuallyproof · cited by 3,134
- IsClosedstatement and proof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- SetRelstatement and proof · cited by 581
- isOpen_compl_iffproof · cited by 63
- SetRel.preimagestatement and proof · cited by 56
- isOpen_iff_eventuallyproof · cited by 3
- IsCompact.eventually_forall_of_forall_eventuallyproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsClosed.relImage_of_isCompactproof · cited by 0