Theorems · Theorem · general topology
TopologicalSpace.Compacts.separableSpace_iff
∀ {α : Type u_1} [inst : TopologicalSpace α],
TopologicalSpace.SeparableSpace (TopologicalSpace.Compacts α) ↔ TopologicalSpace.SeparableSpace α- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 85 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.
Cites23
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
- Set.imageproof · cited by 5,609
- Set.Nonemptyproof · cited by 2,627
- IsOpenproof · cited by 2,400
- IsEmptyproof · cited by 759
- Set.Countableproof · cited by 545
- TopologicalSpace.Compactsstatement and proof · cited by 386
- Set.mem_image_of_memproof · cited by 371
- Set.inter_subset_leftproof · cited by 360
Cited by1
Results whose statement or proof uses this declaration.
- TopologicalSpace.NonemptyCompacts.separableSpace_iffproof · cited by 0