Yes exposure is important.
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In the top 10 there are 6 people from countries of ex Soviet Union (Aronia, Kramnik, Radjabov, Karjakin, Topalov, Mamedyarov), and the other are all from different countries, and if we see the top 100 we can found a lot of people from ex-soviet contries. So top chess isn't only raw talent, but also having great teacher and trainers and begin to play at a very early age.