Theorems · Theorem · general topology
isDiscrete_of_codiscreteWithin
∀ {X : Type u_1} [inst : TopologicalSpace X] {U s : Set X}, sᶜ ∈ Filter.codiscreteWithin U → IsDiscrete (s ∩ U)If s is codiscrete within U, then sᶜ ∩ U has discrete topology.
- Defined in
- Mathlib.Topology.DiscreteSubset
- Cited by
- 3 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.
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
- Filter.principalproof · cited by 740
- compl_complproof · cited by 229
- Filter.codiscreteWithinstatement and proof · cited by 87
- IsDiscretestatement and proof · cited by 86
- Set.compl_unionproof · cited by 30
- sdiff_complproof · cited by 8
Cited by3
Results whose statement or proof uses this declaration.
- ae_restrict_le_codiscreteWithinproof · cited by 4
- MeromorphicOn.countable_compl_analyticAt_interproof · cited by 1
- Function.locallyFinsuppWithin.discreteSupportproof · cited by 1