Theorems · Inductive type · Lie groups
ContinuousVAdd
(M : Type u_1) → (X : Type u_2) → [VAdd M X] → [TopologicalSpace M] → [TopologicalSpace X] → Prop
Class ContinuousVAdd M X says that the additive action (+ᵥ) : M → X → X
is continuous in both arguments. We use the same class for all kinds of additive actions,
including (semi)modules and algebras.
- Defined in
- Mathlib.Topology.Algebra.MulAction
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- VAddstatement · cited by 616
Cited by57
Results whose statement or proof uses this declaration.
- ContinuousVAdd.continuous_vaddstatement and proof · cited by 13
- Continuous.fun_vaddstatement · cited by 9
- ContinuousAffineMap.lineMapstatement and proof · cited by 8
- Continuous.vaddstatement and proof · cited by 6
- Filter.Tendsto.vaddstatement and proof · cited by 6
- IsClosed.vadd_left_of_isCompactstatement and proof · cited by 5
- AddTorsor.connectedSpacestatement and proof · cited by 4
- aeconst_of_dense_setOfPred_preimage_vadd_aestatement and proof · cited by 4
- aeconst_of_dense_setOfPred_preimage_vadd_eqstatement and proof · cited by 3
- ContinuousWithinAt.vaddstatement and proof · cited by 2
- vadd_set_closure_subsetstatement and proof · cited by 2
- IsCompact.vadd_setstatement and proof · cited by 2