Theorems · Theorem · Lie groups
IsOpen.mul_right
∀ {α : Type u} [inst : TopologicalSpace α] [inst_1 : Group α] [ContinuousConstSMul αᵐᵒᵖ α] {s t : Set α},
IsOpen s → IsOpen (s * t)- Defined in
- Mathlib.Topology.Algebra.Group.Pointwise
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 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
- Groupstatement and proof · cited by 6,238
- IsOpenstatement and proof · cited by 2,400
- MulOppositestatement and proof · cited by 1,135
- ContinuousConstSMulstatement and proof · cited by 832
- Set.mulstatement · cited by 297
- IsOpen.smul_leftproof · cited by 3
- Set.image_op_smulproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsOpen.mul_closureproof · cited by 2
- subset_interior_mul_leftproof · cited by 1
- MeasureTheory.Measure.IsEverywherePos.IsGdelta_of_isMulLeftInvariantproof · cited by 1