Theorems · Theorem · general topology
TopologicalSpace.vietoris.specializes_iff
∀ {α : Type u_1} [inst : TopologicalSpace α] {s t : Set α}, s ⤳ t ↔ (∀ x ∈ s, ∃ y ∈ t, x ⤳ y) ∧ t ⊆ closure s- Defined in
- Mathlib.Topology.Sets.VietorisTopology
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 78 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.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.Nonemptyproof · cited by 2,627
- IsOpenproof · cited by 2,400
- closurestatement and proof · cited by 1,254
- Set.mem_image_of_memproof · cited by 371
- subset_closureproof · cited by 309
- isClosed_closureproof · cited by 195
- Specializesstatement and proof · cited by 176
- Set.powersetproof · cited by 67
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.