Theorems · Theorem · general topology
IsNowhereDense.isMeagre
∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsNowhereDense s → IsMeagre sA nowhere dense set is meagre.
- Defined in
- Mathlib.Topology.GDelta.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
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Cites6
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
- IsMeagrestatement · cited by 18
- Set.sUnion_singletonproof · cited by 17
- IsNowhereDensestatement and proof · cited by 15
- isMeagre_iff_countable_union_isNowhereDenseproof · cited by 3
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