Mathlib Map

Theorems · Theorem · functional analysis

ContinuousLinearMap.ext_ring

∀ {R₁ : Type u_1} [inst : Semiring R₁] {M₁ : Type u_4} [inst_1 : TopologicalSpace M₁] [inst_2 : AddCommMonoid M₁]
  [inst_3 : Module R₁ M₁] [inst_4 : TopologicalSpace R₁] {f g : R₁ →L[R₁] M₁}, f 1 = g 1 → f = g
Defined in
Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Basic
Cited by
16 results in Mathlib
Foundations
Depth 24 from the axioms · uses Quot.sound
Assumes
SemiringTopologicalSpaceAddCommMonoidModuleTopologicalSpace

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ContinuousLinearMap.toSpanSingleton_apply_map_one · cited by 5ContinuousLinearMap.toSpa…ContinuousLinearMap.toSpanSingleton_zero · cited by 5ContinuousLinearMap.toSpa…HasDerivAt.star_conj · cited by 3HasDerivAt.star_conjContinuousLinearMap.toSpanSingleton_pow · cited by 3ContinuousLinearMap.toSpa…HasDerivAt.comp_semilinear · cited by 2HasDerivAt.comp_semilinearIsOpen.exists_is_const_of_deriv_eq_zero · cited by 1IsOpen.exists_is_const_of…Real.hasDerivAt_fourier · cited by 1Real.hasDerivAt_fourierContinuousLinearMap.adjoint_innerSL_apply · cited by 1ContinuousLinearMap.adjoi…HasDerivAtFilter.hasGradientAtFilter · cited by 1HasDerivAtFilter.hasGradi…ContinuousLinearMap.intrinsicStar_toSpanSingleton · cited by 0ContinuousLinearMap.intri…InnerProductSpace.rankOne_one_right_eq_toSpanSingleton · cited by 0InnerProductSpace.rankOne…ContinuousLinearMap.ext_ring_iff · cited by 0ContinuousLinearMap.ext_r…RCLike.map_from_real · cited by 0RCLike.map_from_realIsOpen.is_const_of_deriv_eq_zero · cited by 0IsOpen.is_const_of_deriv_…IsOpen.eqOn_of_deriv_eq · cited by 0IsOpen.eqOn_of_deriv_eqDFunLike.coe · cited by 62936DFunLike.coeTopologicalSpace · cited by 24529TopologicalSpaceModule · cited by 20661ModuleRingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAddCommMonoid · cited by 12281AddCommMonoidContinuousLinearMap · cited by 5352ContinuousLinearMapLinearMap.ext_ring · cited by 152LinearMap.ext_ringContinuousLinearMap.coe_inj · cited by 11ContinuousLinearMap.coe_i…ContinuousLinearMap.ext_ringCITED BYCITES

Cites9

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Cited by16

Results whose statement or proof uses this declaration.