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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Solution Summary
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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