Theorems · Theorem · functional analysis
LinearMap.continuous_on_pi
∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} [Finite ι] [inst : Semiring R] [inst_1 : TopologicalSpace R]
[inst_2 : AddCommMonoid M] [inst_3 : Module R M] [inst_4 : TopologicalSpace M] [ContinuousAdd M] [ContinuousSMul R M]
(f : (ι → R) →ₗ[R] M), Continuous ⇑f- Defined in
- Mathlib.Topology.Algebra.Module.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- Fintypeproof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- Continuousstatement and proof · cited by 2,592
Cited by3
Results whose statement or proof uses this declaration.
- Set.Finite.isCompact_convexHullproof · cited by 3
- Real.smul_map_diagonal_volume_piproof · cited by 1
- Real.map_matrix_volume_pi_eq_smul_volume_piproof · cited by 1