Is it possible for a set to be both open and closed in the Zariski topology over the complex affine or projective space?
2026-04-29 00:53:57.1777424037
Clopen sets in Zariski Topology
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I realized the [elemntary] answer, if a set and its complement are closed, then the whole space being the algebraic set of the equation 0=0 can be written as a union (pairwise multiplication) of two sets of equations. however one of them would must be zero in order to recover such a multiplication.