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## Main Question or Discussion Point

Hello,

I am having trouble finding an example of a set in R^2 that is neither open nor closed. I have already shown the half open interval [0,1) is neither open nor closed, but I can't seem to find any other examples. Can someone push me in the right direction? Would x^2+ y^2<1 be open nor closed? Is using the def. of a ball/neighborhood the right way to go to prove this?

I am having trouble finding an example of a set in R^2 that is neither open nor closed. I have already shown the half open interval [0,1) is neither open nor closed, but I can't seem to find any other examples. Can someone push me in the right direction? Would x^2+ y^2<1 be open nor closed? Is using the def. of a ball/neighborhood the right way to go to prove this?