Theorems · Theorem · functional analysis
ContinuousAlternatingMap.map_coord_zero
∀ {R : Type u_1} {M : Type u_2} {N : Type u_4} {ι : Type u_6} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M] [inst_3 : TopologicalSpace M] [inst_4 : AddCommMonoid N] [inst_5 : Module R N]
[inst_6 : TopologicalSpace N] (f : M [⋀^ι]→L[R] N) {m : ι → M} (i : ι), m i = 0 → f m = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
- DFunLike.coestatement · cited by 62,936
- TopologicalSpacestatement and proof · cited by 24,529
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- ContinuousAlternatingMapstatement and proof · cited by 292
- ContinuousAlternatingMap.toContinuousMultilinearMapproof · cited by 72
- ContinuousMultilinearMap.toMultilinearMapproof · cited by 70
- MultilinearMap.map_coord_zeroproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- extDerivWithin_apply_vectorField_of_pairwise_commuteproof · cited by 1