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According to his colleague Alexander Lubotzky, Weisfeiler was studying "the more difficult questions" of algebraic groups in "the case when the field is not algebraically closed and the groups do not split or — even worse — are nonisotropic".
It occurs in the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space has a basis, Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that every nonzero ring has a maximal ideal and that every field has an algebraic closure.