Stochastic Independence, Algebraic Independence and Connectedness
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چکیده
Mutual stochastic independences among-algebras and mutual algebraic inde-pendences among elements of semimodular lattices are observed to have a very similar behaviour. We suggest abstract independence structures called I-relations describing it. Presented examination of I-relations resembles a theory of abstract connectedness: a dual characterization of I-relations by families of connected sets is found by means of a special Galois connection. Representations of I-relations in the matroid theory sense by-algebras and by elements of lattices are discussed.
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