Theorems · Theorem · general topology
TopologicalSpace.NonemptyCompacts.locallyCompactSpace_iff
∀ {α : Type u_1} [inst : TopologicalSpace α],
LocallyCompactSpace (TopologicalSpace.NonemptyCompacts α) ↔ LocallyCompactSpace α- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 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.
Cites24
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
- SetLike.coeproof · cited by 8,199
- Set.ofPredproof · cited by 6,101
- nhdsproof · cited by 5,554
- Set.preimageproof · cited by 4,946
- Set.iUnionproof · cited by 2,483
- Filter.univ_mem'proof · cited by 1,672
- Filter.mp_memproof · cited by 1,537
- IsCompactproof · cited by 1,282
- interiorproof · cited by 714
- LocallyCompactSpacestatement and proof · cited by 324
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.Compacts.locallyCompactSpace_iffproof · cited by 0