1. The problem statement, all variables and given/known data Show that the set S of all (x,y) ∈ ℝ2such that 2x2+xy+y2 is closed but not compact. 2. Relevant equations set S of all (x,y) ∈ ℝ2such that 2x2+xy+y2 3. The attempt at a solution I set x = 0 and then y = 0 giving me [0,±√3] and [±√3,0] which means it is closed However, for it to be Compact, it needs to be Closed & Bounded. For it to be bounded, it must have both an upper and lower bound, which to me it appears to have? The bound for me are when x and y = ±√3 Clearly I am wrong, given how the question is structured. Any ideas?