= Schemes are Kolmogorov spaces
The underlying <topological space> of every <scheme> is a <Kolmogorov space>: any two distinct points are distinguished by an <open subset> containing just one. Choose an <affine open subscheme> containing the first point. If it omits the second, it already distinguishes them. Otherwise, the two points correspond to distinct <prime ideals>, and an element in one but not the other defines a <principal open subscheme> distinguishing them. Thus distinct points of a <scheme> have distinct <closures>.
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