So I have an exam in Real Analysis I coming up next week and I was hoping if someone can help me out. I hope my question makes sense because I think I might be confused with defining the metric space or so... 1. The problem statement, all variables and given/known data a)Suppose that we have a metric space M with the discrete metric d(x,y) = 1 if x = y d(x,y) = 0 if x =/= y Is this open or closed? b)Suppose that we are in R (the real line) and the metric is define as d(x,y) = 1 if x = y d(x,y) = 0 if x =/= y Is this open or closed? 2. Relevant equations Definition: A set is Y open if every point in Y is an interior point A set is Y closed if every point in Y is an limit point 3. The attempt at a solution a)Im not even sure if question a makes sense because I didn't define the metric. b) I'm pretty sure it is open and closed because both the definitions work.