For example , some authors require that an `` algebraic variety '' is , by definition , irreducible ( which means that it is not the union of two smaller sets that are closed in the Zariski topology ) , while others do not .
Conventions regarding the definition of an algebraic variety differ : Some authors require that an `` algebraic variety '' is , by definition , irreducible ( which means that it is not the union of two smaller sets that are closed in the Zariski topology ) , while others do not .