Indexed product of uniform spaces
@[instance]
def
Pi.uniform_space
{ι : Type u_1}
(α : ι → Type u)
[U : Π (i : ι), uniform_space (α i)] :
uniform_space (Π (i : ι), α i)
theorem
Pi.uniform_continuous_proj
{ι : Type u_1}
(α : ι → Type u)
[U : Π (i : ι), uniform_space (α i)]
(i : ι) :
uniform_continuous (λ (a : Π (i : ι), α i), a i)
@[instance]
def
Pi.complete
{ι : Type u_1}
(α : ι → Type u)
[U : Π (i : ι), uniform_space (α i)]
[∀ (i : ι), complete_space (α i)] :
complete_space (Π (i : ι), α i)
@[instance]
def
Pi.separated
{ι : Type u_1}
(α : ι → Type u)
[U : Π (i : ι), uniform_space (α i)]
[∀ (i : ι), separated_space (α i)] :
separated_space (Π (i : ι), α i)