Determine with justification which sets are open, closed, or neither(adsbygoogle = window.adsbygoogle || []).push({});

i) {(x,y,z): x^2+ y^2 + z^2 +(xyz)^2 >= -1}

ii) {(x,y,z): x^2 + y^2 +z^2 >= 1}

iii) {(x,y,z): x^2- y- z >1}

iv) {(x,y): 3>= x^2- xy + y^2 >1

v) {(x,y): x^2 - y^2 >=0 }

So, my first insinct is to go about it using the definition of open sets. So I try and find a neighbourhood around a point in the set that is not completely contained in the set. What confuses me is that that method is not very definite. What if I cant find that neighbourhood?

Any help on how I should go about starting this question off?

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# Which sets are open, closed, or neither?

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