A theorem on doubly transitive permutation groups with application to universal algebras
G. Grätzer (1964)
Fundamenta Mathematicae
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G. Grätzer (1964)
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We establish that for a fairly general class of topologically transitive dynamical systems, the set of non-transitive points is very small when the rate of transitivity is very high. The notion of smallness that we consider here is that of σ-porosity, and in particular we show that the set of non-transitive points is σ-porous for any subshift that is a factor of a transitive subshift of finite type, and for the tent map of [0,1]. The result extends to some finite-to-one factor systems....
W. Nöbauer (1982)
Banach Center Publications
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