Documentation

Mathlib.Topology.Algebra.IsUniformGroup.Constructions

Constructions of new uniform groups from old ones #

theorem isUniformGroup_sInf {G : Type u_1} [Group G] {us : Set (UniformSpace G)} (h : uus, IsUniformGroup G) :
theorem isUniformAddGroup_sInf {G : Type u_1} [AddGroup G] {us : Set (UniformSpace G)} (h : uus, IsUniformAddGroup G) :
@[deprecated isUniformAddGroup_sInf (since := "2025-03-31")]
theorem uniformAddGroup_sInf {G : Type u_1} [AddGroup G] {us : Set (UniformSpace G)} (h : uus, IsUniformAddGroup G) :

Alias of isUniformAddGroup_sInf.

@[deprecated isUniformGroup_sInf (since := "2025-03-31")]
theorem uniformGroup_sInf {G : Type u_1} [Group G] {us : Set (UniformSpace G)} (h : uus, IsUniformGroup G) :

Alias of isUniformGroup_sInf.

theorem isUniformGroup_iInf {G : Type u_1} [Group G] {ι : Sort u_4} {us' : ιUniformSpace G} (h' : ∀ (i : ι), IsUniformGroup G) :
theorem isUniformAddGroup_iInf {G : Type u_1} [AddGroup G] {ι : Sort u_4} {us' : ιUniformSpace G} (h' : ∀ (i : ι), IsUniformAddGroup G) :
@[deprecated isUniformAddGroup_iInf (since := "2025-03-31")]
theorem uniformAddGroup_iInf {G : Type u_1} [AddGroup G] {ι : Sort u_4} {us' : ιUniformSpace G} (h' : ∀ (i : ι), IsUniformAddGroup G) :

Alias of isUniformAddGroup_iInf.

@[deprecated isUniformGroup_iInf (since := "2025-03-31")]
theorem uniformGroup_iInf {G : Type u_1} [Group G] {ι : Sort u_4} {us' : ιUniformSpace G} (h' : ∀ (i : ι), IsUniformGroup G) :

Alias of isUniformGroup_iInf.

theorem isUniformGroup_inf {G : Type u_1} [Group G] {u₁ u₂ : UniformSpace G} (h₁ : IsUniformGroup G) (h₂ : IsUniformGroup G) :
theorem isUniformAddGroup_inf {G : Type u_1} [AddGroup G] {u₁ u₂ : UniformSpace G} (h₁ : IsUniformAddGroup G) (h₂ : IsUniformAddGroup G) :
@[deprecated isUniformAddGroup_inf (since := "2025-03-31")]
theorem uniformAddGroup_inf {G : Type u_1} [AddGroup G] {u₁ u₂ : UniformSpace G} (h₁ : IsUniformAddGroup G) (h₂ : IsUniformAddGroup G) :

Alias of isUniformAddGroup_inf.

@[deprecated isUniformGroup_inf (since := "2025-03-31")]
theorem uniformGroup_inf {G : Type u_1} [Group G] {u₁ u₂ : UniformSpace G} (h₁ : IsUniformGroup G) (h₂ : IsUniformGroup G) :

Alias of isUniformGroup_inf.

theorem IsUniformInducing.isUniformGroup {G : Type u_1} {H : Type u_2} {hom : Type u_3} [Group G] [Group H] [UniformSpace G] [UniformSpace H] [IsUniformGroup H] [FunLike hom G H] [MonoidHomClass hom G H] (f : hom) (hf : IsUniformInducing f) :
theorem IsUniformInducing.isUniformAddGroup {G : Type u_1} {H : Type u_2} {hom : Type u_3} [AddGroup G] [AddGroup H] [UniformSpace G] [UniformSpace H] [IsUniformAddGroup H] [FunLike hom G H] [AddMonoidHomClass hom G H] (f : hom) (hf : IsUniformInducing f) :
@[deprecated IsUniformInducing.isUniformAddGroup (since := "2025-03-30")]
theorem IsUniformInducing.uniformAddGroup {G : Type u_1} {H : Type u_2} {hom : Type u_3} [AddGroup G] [AddGroup H] [UniformSpace G] [UniformSpace H] [IsUniformAddGroup H] [FunLike hom G H] [AddMonoidHomClass hom G H] (f : hom) (hf : IsUniformInducing f) :

Alias of IsUniformInducing.isUniformAddGroup.

@[deprecated IsUniformInducing.isUniformGroup (since := "2025-03-30")]
theorem IsUniformInducing.uniformGroup {G : Type u_1} {H : Type u_2} {hom : Type u_3} [Group G] [Group H] [UniformSpace G] [UniformSpace H] [IsUniformGroup H] [FunLike hom G H] [MonoidHomClass hom G H] (f : hom) (hf : IsUniformInducing f) :

Alias of IsUniformInducing.isUniformGroup.

theorem IsUniformGroup.comap {G : Type u_1} {H : Type u_2} {hom : Type u_3} [Group G] [Group H] {u : UniformSpace H} [IsUniformGroup H] [FunLike hom G H] [MonoidHomClass hom G H] (f : hom) :
theorem IsUniformAddGroup.comap {G : Type u_1} {H : Type u_2} {hom : Type u_3} [AddGroup G] [AddGroup H] {u : UniformSpace H} [IsUniformAddGroup H] [FunLike hom G H] [AddMonoidHomClass hom G H] (f : hom) :
instance Prod.instIsUniformGroup {G : Type u_1} {H : Type u_2} [Group G] [Group H] [UniformSpace G] [hG : IsUniformGroup G] [UniformSpace H] [hH : IsUniformGroup H] :
@[deprecated Prod.instIsUniformAddGroup (since := "2025-03-31")]

Alias of Prod.instIsUniformAddGroup.

@[deprecated Prod.instIsUniformGroup (since := "2025-03-31")]
theorem Prod.instUniformGroup {G : Type u_1} {H : Type u_2} [Group G] [Group H] [UniformSpace G] [hG : IsUniformGroup G] [UniformSpace H] [hH : IsUniformGroup H] :

Alias of Prod.instIsUniformGroup.

instance Pi.instIsUniformGroup {ι : Type u_4} {G : ιType u_5} [(i : ι) → UniformSpace (G i)] [(i : ι) → Group (G i)] [∀ (i : ι), IsUniformGroup (G i)] :
IsUniformGroup ((i : ι) → G i)
instance Pi.instIsUniformAddGroup {ι : Type u_4} {G : ιType u_5} [(i : ι) → UniformSpace (G i)] [(i : ι) → AddGroup (G i)] [∀ (i : ι), IsUniformAddGroup (G i)] :
IsUniformAddGroup ((i : ι) → G i)

The discrete uniformity makes a group a `IsUniformGroup.

The discrete uniformity makes an additive group a IsUniformAddGroup.