Theorems · Theorem · Lie groups
IsOpen.leftCoset
∀ {G : Type w} [inst : TopologicalSpace G] [inst_1 : Group G] [SeparatelyContinuousMul G] {U : Set G},
IsOpen U → ∀ (x : G), IsOpen (x • U)- Defined in
- Mathlib.Topology.Algebra.Group.Basic
- Cited by
- 2 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.
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
- Groupstatement and proof · cited by 6,238
- IsOpenstatement and proof · cited by 2,400
- Set.smulSetstatement · cited by 608
- SeparatelyContinuousMulstatement and proof · cited by 133
- isOpenMap_mul_leftproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- ProfiniteGrp.toLimitFun_continuousproof · cited by 0
- krullTopology_t2proof · cited by 0