We can also describe the collection of lines in R2 that intersect the origin by means of a topological construction. To wit: consider S1 ⊂ R2 and notice that every point "s" ∈ S1 gives a line "L"("s") in the collection (which joins the origin and "s"). However, this map is two-to-one, so we want to identify "s" ~ −"s" to yield P1(R) ≅ S1/~ where the topology on this space is the quotient topology induced by the quotient map S1 → P1(R).