Some Notions of Size in Partial Semigroups
نویسنده
چکیده
In a semigroup, the combinatorial definitions of syndetic, piecewise syndetic, and IP are equivalent to their algebraic characterizations in terms of βS. We introduce the analogous definitions and characterizations of syndetic, piecewise syndetic, and IP for an adequate partial semigroup and show that equivalence between the combinatorial definition and algebraic characterization is lost once we move from a semigroup to a partial semigroup. Where they exist, we show some of the interrelationships between the notions; and in the case of IP, we give some conditions for when the algebraic characterization and combinatorial definition are in fact equivalent.
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