Theorems · Definition · general topology
IsNowhereDense
{X : Type u_1} → [TopologicalSpace X] → Set X → PropA set is called nowhere dense iff its closure has empty interior.
- Defined in
- Mathlib.Topology.GDelta.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- closureproof · cited by 1,254
- interiorproof · cited by 714
Cited by15
Results whose statement or proof uses this declaration.
- isMeagre_iff_countable_union_isNowhereDensestatement and proof · cited by 3
- IsClosed.isNowhereDense_iffstatement · cited by 2
- Topology.IsInducing.isNowhereDense_imagestatement and proof · cited by 2
- IsNowhereDense.closurestatement and proof · cited by 2
- Topology.IsInducing.isMeagre_imageproof · cited by 1
- isNowhereDense_iff_forall_notMem_nhdsstatement · cited by 1
- IsNowhereDense.of_isClosed_nullstatement · cited by 1
- IsMeagre.of_isSigmaCompact_nullproof · cited by 0
- isClosed_isNowhereDense_iff_complstatement · cited by 0
- isNowhereDense_emptystatement · cited by 0
- isNowhereDense_iff_disjointstatement and proof · cited by 0
- IsNowhereDense.image_valstatement and proof · cited by 0