Show that the set S of all (x,y) ∈ ℝ2such that 2x2+xy+y2
is closed but not compact.
set S of all (x,y) ∈ ℝ2such that 2x2+xy+y2
The Attempt at a Solution
I set x = 0 and then y = 0
[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?