The book I am reading, Linear Algebraic Groups by Humphreys defines a prevariety X in projective space P^n to be a noetherian topological space endowed with a sheaf of functions such that X is the union of finitely many open subsets, each isomorphic to an affine variety.(adsbygoogle = window.adsbygoogle || []).push({});

This confuses me because I do not understand how affine varieties, which are closed sets in the Zariski topology, can be isomorphic to open sets in P^n.

Please help! :yuck:

Daniel

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definition of Prevariety

**Physics Forums | Science Articles, Homework Help, Discussion**