English
From a filter basis B on α × α with coherence, define UniformSpace.Core α using B.filter as uniformity and preserving the coherence conditions.
Русский
Из базиса фильтров B на α×α с когерентностью определить UniformSpace.Core α, используя B.filter как равномерность и сохраняя условия когерентности.
LaTeX
$$$\\text{Given } B: FilterBasis(\\alpha\\times\\alpha)\\text{ with reflexive, symmetric, and comp properties } UniformSpace.Core\\,\\alpha$$$
Lean4
/-- The uniformity is a filter on α × α (inferred from an ambient uniform space
structure on α). -/
def uniformity (α : Type u) [UniformSpace α] : Filter (α × α) :=
@UniformSpace.uniformity α _
