Theorems · Theorem · general topology
closure_mono
∀ {X : Type u} [inst : TopologicalSpace X] {s t : Set X}, s ⊆ t → closure s ⊆ closure t- Defined in
- Mathlib.Topology.Closure
- Cited by
- 133 results in Mathlib
- Foundations
- Depth 66 from the axioms, rests on 700 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- subset_closureproof · cited by 309
- Set.Subset.transproof · cited by 218
- isClosed_closureproof · cited by 195
- closure_minimalproof · cited by 94
Cited by133
Results whose statement or proof uses this declaration.
- Dense.monoproof · cited by 43
- IsCompact.closure_of_subsetproof · cited by 15
- isClosed_propertyproof · cited by 13
- Continuous.closure_preimage_subsetproof · cited by 12
- UniqueDiffWithinAt.monoproof · cited by 8
- TopologicalSpace.IsSeparable.iUnionproof · cited by 7
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- Real.sin_nonneg_of_mem_Iccproof · cited by 6
- monotone_closureproof · cited by 5
- BumpCovering.IsSubordinate.toPartitionOfUnityproof · cited by 5
- Submodule.topologicalClosure_monoproof · cited by 5
- closure_Iocproof · cited by 5