Theorems · Theorem · general topology
Topology.IsEmbedding.image_mem_codiscreteWithin
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
Topology.IsEmbedding f → ∀ {s t : Set X}, f '' s ∈ Filter.codiscreteWithin (f '' t) ↔ s ∈ Filter.codiscreteWithin t- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 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
- Filterstatement and proof · cited by 8,121
- Set.imagestatement and proof · cited by 5,609
- Filter.principalproof · cited by 740
- Topology.IsEmbeddingstatement and proof · cited by 294
- Set.image_singletonproof · cited by 174
- ClusterPtproof · cited by 138
- Topology.IsEmbedding.injectiveproof · cited by 103
- Filter.codiscreteWithinstatement · cited by 87
- Topology.IsEmbedding.toIsInducingproof · cited by 48
- Set.image_sdiffproof · cited by 24
Cited by1
Results whose statement or proof uses this declaration.
- Topology.IsEmbedding.image_mem_codiscreteWithin_rangeproof · cited by 1