Mathlib Map

Theorems · Theorem · general topology

IsNowhereDense.closure

∀ {X : Type u_1} [inst : TopologicalSpace X] {s : Set X}, IsNowhereDense s → IsNowhereDense (closure s)

If a set s is nowhere dense, so is its closure.

Defined in
Mathlib.Topology.GDelta.Basic
Cited by
2 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isMeagre_iff_countable_union_isNowhereDense · cited by 3isMeagre_iff_countable_un…IsNowhereDense.subset_of_closed_isNowhereDense · cited by 0IsNowhereDense.subset_of_…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceclosure · cited by 1254closureinterior · cited by 714interiorIsNowhereDense · cited by 15IsNowhereDenseclosure_closure · cited by 9closure_closureIsNowhereDense.closureCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.