Theorems · Theorem · general topology
TopologicalSpace.Opens.isCompactElement_iff
∀ {α : Type u_2} [inst : TopologicalSpace α] (s : TopologicalSpace.Opens α), IsCompactElement s ↔ IsCompact ↑s- Defined in
- Mathlib.Topology.Sets.Opens
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 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.
Cites21
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
- Finsetproof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.iUnionproof · cited by 2,483
- iSupproof · cited by 2,415
- IsOpenproof · cited by 2,400
- le_reflproof · cited by 2,061
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- IsCompactstatement · cited by 1,282
- Finset.supproof · cited by 530
- Set.Subset.transproof · cited by 218
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.noetherianSpace_iff_opensproof · cited by 3