open sets in metric spaces
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
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.
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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