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Theorems · Theorem · Lie groups

uniformity_eq_comap_nhds_zero

∀ (Gᵣ : Type u_3) [inst : UniformSpace Gᵣ] [inst_1 : AddGroup Gᵣ] [IsRightUniformAddGroup Gᵣ],
  uniformity Gᵣ = Filter.comap (fun x => x.2 - x.1) (nhds 0)
Defined in
Mathlib.Topology.Algebra.IsUniformGroup.Defs
Cited by
17 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
UniformSpaceAddGroupIsRightUniformAddGroup

Around this declaration

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

cauchySeq_finset_iff_sum_vanishing · cited by 5cauchySeq_finset_iff_sum_…Filter.HasBasis.uniformity_of_nhds_zero · cited by 4HasBasis.uniformity_of_nh…uniformity_eq_comap_nhds_zero_swapped · cited by 4uniformity_eq_comap_nhds_…Valued.hasBasis_uniformity · cited by 4Valued.hasBasis_uniformityDisjoint.exists_open_convexes · cited by 2Disjoint.exists_open_conv…uniformContinuous_of_tendsto_zero · cited by 2uniformContinuous_of_tend…AddGroupFilterBasis.cauchy_iff · cited by 2AddGroupFilterBasis.cauch…IsUniformAddGroup.ext · cited by 2IsUniformAddGroup.extIsUniformAddGroup.uniformity_countably_generated · cited by 2IsUniformAddGroup.uniform…AddMonoidHom.isUniformInducing_of_isInducing · cited by 2AddMonoidHom.isUniformInd…IsDenseInducing.extend_Z_bilin · cited by 1IsDenseInducing.extend_Z_…LaurentSeries.inducing_coe · cited by 1LaurentSeries.inducing_coeValuation.hasBasis_uniformity · cited by 1Valuation.hasBasis_unifor…NonarchimedeanAddGroup.cauchySeq_of_tendsto_sub_nhds_zero · cited by 0NonarchimedeanAddGroup.ca…IsUniformAddGroup.cauchy_iff_tendsto_swapped · cited by 0IsUniformAddGroup.cauchy_…Filter · cited by 8121Filternhds · cited by 5554nhdsAddGroup · cited by 4410AddGroupUniformSpace · cited by 2040UniformSpacesub_eq_add_neg · cited by 1023sub_eq_add_neguniformity · cited by 765uniformityFilter.comap · cited by 546Filter.comapIsRightUniformAddGroup · cited by 9IsRightUniformAddGroupuniformity_eq_comap_add_neg_nhds_zero · cited by 4uniformity_eq_comap_add_n…uniformity_eq_comap_nhds_zeroCITED BYCITES

Cites9

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Cited by17

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