English
SeparatedNhds is a predicate on pairs of subsets of a topological space; it holds if the two subsets can be placed in disjoint open sets.
Русский
SeparatedNhds — предикат на парах подмножеств пространства; он истинно, если их можно поместить в дисjoint открытые множества.
LaTeX
$$$\\text{SeparatedNhds} : \\text{Set } X \\to \\text{Set } X \\to \\text{Prop} := \\lambda s t, \\exists U V, \\IsOpen U \\land \\IsOpen V \\land s \\subseteq U \\land t \\subseteq V \\land \\text{Disjoint } U V$$$
Lean4
/-- `SeparatedNhds` is a predicate on pairs of sub`Set`s of a topological space. It holds if the two
sub`Set`s are contained in disjoint open sets.
-/
def SeparatedNhds : Set X → Set X → Prop := fun s t : Set X =>
∃ U V : Set X, IsOpen U ∧ IsOpen V ∧ s ⊆ U ∧ t ⊆ V ∧ Disjoint U V
