1. The problem statement, all variables and given/known data Define a quasimetric on the Sorgenfrey Line. 2. Relevant equations I know how to show the distance function is always nonnegative, equal to zero if evaluating the distance of a point from itself, and the triangle inequality. I'm having trouble coming up with the function. 3. The attempt at a solution I have defined d(p,q) = q - p (if q > p) and 0 otherwise. I want to show that the sphere centered at p of radius e is the same as the interval [p, p+e). This will complete the proof. Suppose x is in the sphere centered at p of radius e. Then either d(p,x) = 0 or d(p,x) < e (IFF) p <= x or x - p < e (IFF) p <= x or x < p + e. What bothers me here is the "or". It feels like I need "and" to justify x in [p, p+e). Help?