Theorems · Theorem · general topology
punctured_nhds_smul
∀ {α : Type u_2} {G : Type u_4} [inst : TopologicalSpace α] [inst_1 : Group G] [inst_2 : MulAction G α]
[ContinuousConstSMul G α] (c : G) (x : α), nhdsWithin (c • x) {c • x}ᶜ = c • nhdsWithin x {x}ᶜ- Defined in
- Mathlib.Topology.Algebra.ConstMulAction
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Filterstatement · cited by 8,121
- Groupstatement and proof · cited by 6,238
- Compl.complstatement · cited by 2,925
- nhdsWithinstatement · cited by 1,912
- MulActionstatement and proof · cited by 1,294
- ContinuousConstSMulstatement and proof · cited by 832
- Homeomorph.smulproof · cited by 21
- Homeomorph.map_punctured_nhds_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- punctured_nhds_smul₀proof · cited by 0