Lecture 14 (Topology)

Given a topological space (X, τ) and a subset Y ⊆ X, how is the subspace topology τ_Y on Y defined?

1. A.τ_Y is the collection of all subsets of Y that are open in X
2. B.τ_Y is the collection of sets U ∩ Y where U ∈ τ
3. C.τ_Y is the collection of closed sets of X restricted to Y
4. D.τ_Y is the smallest topology on Y containing every element of τ