open sets in metric spaces Watch

lmassey
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Hey does anyone know how to answer this question. Decide weather A={(x1, x2, x3) E R^3 : x1^2 + x2^2 E (-infinity, 1] and x3=1} is an open, closed, both, or neither open or closed subset in X=R^3 with the usual exclude an metric d2
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ghostwalker
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(Original post by lmassey)
Hey does anyone know how to answer this question. Decide weather A={(x1, x2, x3) E R^3 : x1^2 + x2^2 E (-infinity, 1] and x3=1} is an open, closed, both, or neither open or closed subset in X=R^3 with the usual exclude an metric d2
Don't understand the phrase in bold. Is this the usual euclidean metric?

Might help to draw the set, then it should be clear.
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lmassey
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Yh i sorry I did mean euclidean
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james22
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Try to picture it. Does it look open or closed?
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lmassey
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I think it's closed just not sure how to prove it .
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james22
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(Original post by lmassey)
I think it's closed just not sure how to prove it .
Your intuition is correct.

What does it mean for a set to be closed? How do you think you would start to prove it?
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