Theorems · Theorem · general topology
subset_closure
∀ {X : Type u} [inst : TopologicalSpace X] {s : Set X}, s ⊆ closure s- Defined in
- Mathlib.Topology.Closure
- Cited by
- 309 results in Mathlib
- Foundations
- Depth 61 from the axioms, rests on 681 definitions · uses propext, Classical.choice, Quot.sound
- 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
- closurestatement · cited by 1,254
- Set.subset_sInterproof · cited by 8
Cited by309
Results whose statement or proof uses this declaration.
- IsClosed.closure_eqproof · cited by 139
- closure_monoproof · cited by 133
- IsClosed.closure_subset_iffproof · cited by 59
- IsCompact.closureproof · cited by 25
- subset_tsupportproof · cited by 21
- dense_univproof · cited by 12
- Continuous.closure_preimage_subsetproof · cited by 12
- isClosed_of_closure_subsetproof · cited by 12
- PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closureproof · cited by 11
- IsCompact.measure_closureproof · cited by 10
- Metric.self_subset_thickeningproof · cited by 10
- MeasureTheory.Measure.addHaarMeasure_uniqueproof · cited by 9
Showing the 200 most cited of 309.