Lecture 8 (Topology)

A collection β of subsets of X is called a basis for a topology on X if it satisfies exactly which two conditions?

1. A.Every x ∈ X lies in some B ∈ β, and for any B₁, B₂ ∈ β with x ∈ B₁ ∩ B₂ there is some B₃ ∈ β with x ∈ B₃ ⊆ B₁ ∩ B₂
2. B.Every B ∈ β is open, and β is closed under finite intersection
3. C.β contains ∅ and X, and β is closed under arbitrary union
4. D.β is finite, and every singleton {x} belongs to β