Theorems · Definition · general topology
Dense
{X : Type u} → [TopologicalSpace X] → Set X → PropA set is dense in a topological space if every point belongs to its closure.
- Defined in
- Mathlib.Topology.Defs.Basic
- Cited by
- 359 results in Mathlib
- Foundations
- Depth 7 from the axioms, rests on 20 definitions · uses no axioms
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
Cited by390
Results whose statement or proof uses this declaration.
- DenseRangeproof · cited by 164
- Dense.monostatement and proof · cited by 43
- AlgebraicGeometry.Scheme.PartialMap.restrictstatement and proof · cited by 31
- dense_iff_closure_eqstatement · cited by 26
- Dense.closure_eqstatement · cited by 24
- residualproof · cited by 23
- AlgebraicGeometry.Scheme.PartialMap.equivproof · cited by 18
- uniqueDiffWithinAt_univproof · cited by 16
- TopologicalSpace.exists_countable_densestatement · cited by 15
- AlgebraicGeometry.Scheme.PartialMap.dense_domainstatement · cited by 14
- dense_iff_inter_openstatement and proof · cited by 13
- Dense.extendstatement and proof · cited by 13
Showing the 200 most cited of 390.