Theorems · Definition · general topology
residual
(X : Type u_5) → [TopologicalSpace X] → Filter X
A set s is called residual if it includes a countable intersection of dense open sets.
- Defined in
- Mathlib.Topology.GDelta.Basic
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 83 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- IsOpenproof · cited by 2,400
- Denseproof · cited by 359
- Filter.countableGenerateproof · cited by 3
Cited by24
Results whose statement or proof uses this declaration.
- IsMeagreproof · cited by 18
- residual_of_dense_Gδstatement · cited by 4
- residual_of_dense_openstatement · cited by 3
- tendsto_residual_of_isOpenMapstatement · cited by 3
- dense_of_mem_residualstatement and proof · cited by 3
- mem_residualstatement · cited by 3
- eventually_residual_liouvillestatement and proof · cited by 2
- mem_residual_iffstatement · cited by 2
- coborder_mem_residualstatement · cited by 1
- BaireMeasurableSet.congrstatement and proof · cited by 1
- eventually_residual_irrationalstatement · cited by 1
- BaireMeasurableSet.of_mem_residualstatement and proof · cited by 1