Theorems · Theorem · general topology
smul_mem_nhds_smul_iff
∀ {α : Type u_2} {G : Type u_4} [inst : TopologicalSpace α] [inst_1 : Group G] [inst_2 : MulAction G α]
[ContinuousConstSMul G α] {t : Set α} (g : G) {a : α}, g • t ∈ nhds (g • a) ↔ t ∈ nhds a- Defined in
- Mathlib.Topology.Algebra.ConstMulAction
- Cited by
- 5 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.
Cites11
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
- Filterstatement · cited by 8,121
- Groupstatement and proof · cited by 6,238
- nhdsstatement · cited by 5,554
- MulActionstatement and proof · cited by 1,294
- ContinuousConstSMulstatement and proof · cited by 832
- Set.smulSetstatement · cited by 608
- Homeomorph.isOpenEmbeddingproof · cited by 28
- Homeomorph.smulproof · cited by 21
- Topology.IsOpenEmbedding.image_mem_nhdsproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- smul_mem_nhds_smulproof · cited by 2
- smul_mem_nhds_smul_iff₀proof · cited by 2
- singleton_mul_mem_nhdsproof · cited by 1
- IsUnit.smul_mem_nhds_smul_iffproof · cited by 0
- smul_mem_nhds_selfproof · cited by 0