Theorems · Theorem · general topology
Set.Subsingleton.mem_codiscreteWithin
∀ {X : Type u_1} [inst : TopologicalSpace X] [T1Space X] {s t : Set X}, t.Subsingleton → s ∈ Filter.codiscreteWithin tIn a T1Space, every set is codiscrete within a subsingleton set.
- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceT1Space
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 8,121
- Set.univproof · cited by 3,945
- Set.extproof · cited by 2,266
- Set.Subsingletonstatement and proof · cited by 276
- T1Spacestatement and proof · cited by 275
- Filter.univ_memproof · cited by 96
- Filter.codiscreteWithinstatement · cited by 87
- Set.Subsingleton.finiteproof · cited by 20
- codiscreteWithin_iff_locallyEmptyComplementWithinproof · cited by 3
- nhdsNE_of_nhdsNE_sdiff_finiteproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- MeromorphicOn.exists_ecanonicalDecompproof · cited by 0