What is the Alexandrov compactification of the following set and give the geometric interpretation of it: [(x,y): x^2-y^2>=1, x>0] that is, the right part of the hyperbola along with the point in it. This is a question from my todays exam in topology. I wrote that the given set is homeomorphic to the set [0,1)x[0,1) the alexandrov compactification of which is [0,1]x[0,1]. However I'm not sure at all. Is this correct?