Lecture 16 (Topology)

Given a topological space (X, τ) and a surjective map p: X → A, how is the quotient topology on A defined?

1. A.V ⊆ A is open iff V is the image of an open set in X
2. B.V ⊆ A is open iff p⁻¹(V) is open in X
3. C.V ⊆ A is open iff every preimage p⁻¹({a}) is open
4. D.V ⊆ A is open iff V is finite