Liu, Yu-Ru2023-10-032023-10-032004-12-01https://doi.org/10.4153/CMB-2004-056-7http://hdl.handle.net/10012/19994This article has been published in a revised form in the Canadian Mathematical Bulletin https://doi.org/10.4153/CMB-2004-056-7. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2004 Canadian Mathematical Bulletin.We axiomatize the main properties of the classical Turan Theorem in order to apply it to a general context. We provide applications in the cases of number fields, function fields, and geometrically irreducible varieties over a finite field.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/11N3711N80Article