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Theorems · Theorem · general topology

AddGroupFilterBasis.isUniformAddGroup

∀ {G : Type u_1} [inst : AddCommGroup G] (B : AddGroupFilterBasis G), IsUniformAddGroup G

The uniform space structure associated to an abelian group filter basis via the associated topological abelian group structure is compatible with its group structure.

Defined in
Mathlib.Topology.Algebra.UniformFilterBasis
Cited by
1 results in Mathlib
Foundations
Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
AddCommGroup
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Around this declaration

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

AddGroupFilterBasis.cauchy_iff · cited by 2AddGroupFilterBasis.cauch…AddCommGroup · cited by 12871AddCommGroupIsUniformAddGroup · cited by 342IsUniformAddGroupAddGroupFilterBasis · cited by 27AddGroupFilterBasisisUniformAddGroup_of_addCommGroup · cited by 21isUniformAddGroup_of_addC…AddGroupFilterBasis.uniformSpace · cited by 2AddGroupFilterBasis.unifo…AddGroupFilterBasis.isUniform…CITED BYCITES

Cites5

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Cited by1

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