Theorems · Theorem · general topology
smul_closure_subset
∀ {M : Type u_1} {α : Type u_2} [inst : TopologicalSpace α] [inst_1 : SMul M α] [ContinuousConstSMul M α] (c : M)
(s : Set α), c • closure s ⊆ closure (c • s)- Defined in
- Mathlib.Topology.Algebra.ConstMulAction
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- ContinuousConstSMulstatement and proof · cited by 832
- Set.smulSetstatement · cited by 608
- Set.mapsTo_imageproof · cited by 71
- Set.MapsTo.image_subsetproof · cited by 49
- ContinuousConstSMul.continuous_const_smulproof · cited by 25
- Set.MapsTo.closureproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Convex.combo_interior_closure_subset_interiorproof · cited by 3
- smul_closure_orbit_subsetproof · cited by 1
- set_smul_closure_subsetproof · cited by 1