Zariski Topology
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High Quality Content by WIKIPEDIA articles! In mathematics, namely algebraic geometry, the Zariski topology is a particular topology chosen for algebraic varieties that reflects the algebraic nature of their definition. It is due to Oscar Zariski and took a place of particular importance in the field around 1950. Joe Harris says in his introductory lectures that it is "not a real topology" and points out that in the Zariski topology, every two algebraic curves are homeomorphic simply because their underlying sets have equal cardinalities and their topologies are both cofinite. Naturally, such…mehr

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High Quality Content by WIKIPEDIA articles! In mathematics, namely algebraic geometry, the Zariski topology is a particular topology chosen for algebraic varieties that reflects the algebraic nature of their definition. It is due to Oscar Zariski and took a place of particular importance in the field around 1950. Joe Harris says in his introductory lectures that it is "not a real topology" and points out that in the Zariski topology, every two algebraic curves are homeomorphic simply because their underlying sets have equal cardinalities and their topologies are both cofinite. Naturally, such a homeomorphism is not a regular map, but this merely highlights the fact that the deep structure of algebraic varieties is mostly encoded in the choice of functions between them rather than of topologies on them.