Theorems · Theorem · general topology
mem_codiscrete
∀ {X : Type u_1} [inst : TopologicalSpace X] {S : Set X},
S ∈ Filter.codiscrete X ↔ ∀ (x : X), Disjoint (nhdsWithin x {x}ᶜ) (Filter.principal Sᶜ)- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 75 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.
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
- Compl.complstatement · cited by 2,925
- Disjointstatement and proof · cited by 2,201
- nhdsWithinstatement and proof · cited by 1,912
- Filter.principalstatement and proof · cited by 740
- inf_of_le_rightproof · cited by 128
- Set.compl_eq_univ_sdiffproof · cited by 43
- Filter.codiscretestatement · cited by 34
- sdiff_sdiff_right_selfproof · cited by 20
Cited by2
Results whose statement or proof uses this declaration.
- mem_codiscrete'proof · cited by 2
- compl_mem_codiscrete_iffproof · cited by 2