Theorems · Theorem · general topology
TopologicalSpace.noetherianSpace_iff_isCompact
∀ {α : Type u_1} [inst : TopologicalSpace α], TopologicalSpace.NoetherianSpace α ↔ ∀ (s : Set α), IsCompact s- Defined in
- Mathlib.Topology.NoetherianSpace
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 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.
Cites10
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
- SetLike.coeproof · cited by 8,199
- TopologicalSpace.Opensproof · cited by 2,040
- IsCompactstatement and proof · cited by 1,282
- WellFoundedLTproof · cited by 491
- List.TFAE.outproof · cited by 177
- TopologicalSpace.Closedsproof · cited by 168
- TopologicalSpace.NoetherianSpacestatement and proof · cited by 23
- TopologicalSpace.noetherianSpace_TFAEproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.noetherianSpace_of_surjectiveproof · cited by 2