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Theorems · Theorem · Lie groups

Continuous.const_add

∀ {M : Type u_1} [inst : TopologicalSpace M] [inst_1 : Add M] [SeparatelyContinuousAdd M] {X : Type u_2}
  [inst_3 : TopologicalSpace X] {f : X → M}, Continuous f → ∀ (b : M), Continuous fun x => b + f x
Defined in
Mathlib.Topology.Algebra.Monoid.Defs
Cited by
26 results in Mathlib
Foundations
Depth 8 from the axioms · uses no axioms
Assumes
TopologicalSpaceAddSeparatelyContinuousAddTopologicalSpace

Around this declaration

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

compact_covered_by_add_left_translates · cited by 4compact_covered_by_add_le…Complex.two_pi_I_inv_smul_circleIntegral_sub_inv_smul_of_differentiable_on_off_countable · cited by 3Complex.two_pi_I_inv_smul…ApproximatesLinearOn.norm_fderiv_sub_le · cited by 3ApproximatesLinearOn.norm…Filter.EventuallyEq.hasLineDerivWithinAt_iff · cited by 3EventuallyEq.hasLineDeriv…Real.circleMap.continuous · cited by 2circleMap.continuousSchwartzMap.eLpNorm_le_seminorm · cited by 2SchwartzMap.eLpNorm_le_se…Filter.EventuallyEq.hasLineDerivAt_iff · cited by 2EventuallyEq.hasLineDeriv…IsLocalExtr.hasLineDerivAt_eq_zero · cited by 2IsLocalExtr.hasLineDerivA…IsLocalExtr.lineDeriv_eq_zero · cited by 2IsLocalExtr.lineDeriv_eq_…ContinuousLinearMap.isOpenMap_of_ne_zero · cited by 2ContinuousLinearMap.isOpe…AnalyticAt.eventually_constant_or_nhds_le_map_nhds · cited by 1AnalyticAt.eventually_con…HasLineDerivWithinAt.hasLineDerivAt · cited by 1HasLineDerivWithinAt.hasL…HasLineDerivWithinAt.mono_of_mem_nhdsWithin · cited by 1HasLineDerivWithinAt.mono…gronwallBound_continuous_ε · cited by 1gronwallBound_continuous_εGaussianFourier.integral_cexp_neg_mul_sq_add_real_mul_I · cited by 1GaussianFourier.integral_…TopologicalSpace · cited by 24529TopologicalSpaceContinuous · cited by 2592ContinuousContinuous.comp · cited by 371Continuous.compSeparatelyContinuousAdd · cited by 83SeparatelyContinuousAddcontinuous_const_add · cited by 23continuous_const_addContinuous.const_addCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by26

Results whose statement or proof uses this declaration.