Zariski topology

In mathematics, the Zariski topology is a structure basic to algebraic geometry, especially since 1950. It is named after its originator, Oscar Zariski.

Related Topics:
Mathematics - Algebraic geometry - Oscar Zariski

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The Zariski topology is defined by defining the closed sets to be the sets consisting of the mutual zeroes of a set of polynomials. (See affine varieties)

Related Topics:
Topology - Closed set - Polynomial - Affine varieties

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This is a topology, because two basic axioms can be checked. The intersection of any number of closed sets is the set of mutual zeros of the union of all the defining polynomials. The union of two closed sets, defined by polynomials Pi and Qj, is the set of mutual zeros of the set of products PiQj.

Related Topics:
Topology - Intersection - Union

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