A point $P$ in a variety $X$ (affine,quasi-affine,projetive,quasi-projective)is closed if the closure $\overline{\{P\}}=\{P\}$.Will someone be kind enough to give me some hints on this?Thank you very much!
Are points in a variety always closed?
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algebraic-geometry
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3Do you know the definition of the Zariski topology? If you understand the definition, then you shouldn't have any problems with the question. If you don't, then that's what you should be asking about. – 2011-08-12
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4@user14242: From the string of questions you have been asking, I'm beginning to get the impression you're trying to run before you can stand, to stretch a metaphor. Anyway. Your question is not clear. What do you mean by a variety—a locally ringed space in the sense of Hartshorne Chapter I, or an integral scheme of finite type over $\operatorname{Spec} k$, for some algebraically closed $k$? – 2011-08-12