1. The problem statement, all variables and given/known data This isn't a homework problem but just a fundamental concept that my entire complex analysis course is based on. The set D = ℂ \ non-positive real axis. Why is it considered open and connected (domain)? 2. Relevant equations 3. The attempt at a solution When it says non-positive real axis, is the origin included? I can see why D is connected. But why is it considered open? The set is open when it contains all of its boundaries. But the set D clearly does not contain any point on the non-positive real axis.