Theorems · Theorem · general topology
TopologicalSpace.NoetherianSpace.isCompact
∀ {α : Type u_1} [inst : TopologicalSpace α] [TopologicalSpace.NoetherianSpace α] (s : Set α), IsCompact sIn a Noetherian space, all sets are compact.
- Defined in
- Mathlib.Topology.NoetherianSpace
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Finsetproof · cited by 13,712
- SetLike.coeproof · cited by 8,199
- LE.le.transproof · cited by 3,151
- Set.iUnionproof · cited by 2,483
- IsOpenproof · cited by 2,400
- IsCompactstatement · cited by 1,282
- Set.Subset.rflproof · cited by 255
- isOpen_iUnionproof · cited by 88
- IsCompact.elim_finite_subcoverproof · cited by 28
- TopologicalSpace.NoetherianSpacestatement and proof · cited by 23
Cited by5
Results whose statement or proof uses this declaration.
- TopologicalSpace.noetherianSpace_of_surjectiveproof · cited by 2
- TopologicalSpace.noetherianSpace_TFAEproof · cited by 1
- Topology.IsInducing.noetherianSpaceproof · cited by 1
- TopologicalSpace.NoetherianSpace.discreteproof · cited by 0
- TopologicalSpace.NoetherianSpace.finiteproof · cited by 0