# Affine Algebraic Sets and Topologies

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1. Show that affine algebraic sets satisfy the axioms for the closed sets of a topology, i.e. show that the intersection of an arbitrary collection of algebraic sets is algebraic and the union of two algebraic sets is algebraic.

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Affine Algebraic Sets and Topologies are investigated. The collection of algebraic sets is algebraic and the union of two algebraic sets is algebraic.

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Proof:

First, I claim that the intersection of an arbitrary collection of algebraic sets is algebraic.

Suppose is an ...

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