Theorems · Theorem · general topology
compl_mem_codiscrete_iff
∀ {X : Type u_1} [inst : TopologicalSpace X] {S : Set X}, Sᶜ ∈ Filter.codiscrete X ↔ IsClosed S ∧ IsDiscrete S- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 77 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.
Cites13
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
- Compl.complstatement and proof · cited by 2,925
- Disjointproof · cited by 2,201
- nhdsWithinproof · cited by 1,912
- IsClosedstatement and proof · cited by 1,639
- Filter.principalproof · cited by 740
- compl_complproof · cited by 229
- IsDiscretestatement and proof · cited by 86
- Filter.codiscretestatement · cited by 34
- mem_codiscreteproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- IsDiscrete.iUnionproof · cited by 3
- codiscrete_le_cofiniteproof · cited by 2