Complex sentence: A nonempty family Δ of finite subsets of a universal set "S" is an abstract simplicial complex if, for every set "X" in Δ, and every subset "Y" ⊂ "X", "Y" also belongs to Δ.
Split into simpler sentences: A nonempty family Δ of finite subsets of a universal set "S" is an abstract simplicial complex if Δ is closed under subsets. That is, Δ is an abstract simplicial complex if, for every set "X" in Δ, and every subset "Y" ⊂ "X", "Y" also belongs to Δ.