Central sets theorem near zero (Q5890836)

The authors introduce the so-called \(J\)-sets near zero and \(C\)-sets near zero (whose definitions are quite technical) for a dense subsemigroup of \(((0, +\infty), +)\), and state the Central Sets Theorem near zero. Among other results for a dense subsemigroup \(S \subseteq((0, +\infty), +)\), they give some sufficient and equivalent algebraic conditions for a subset \(A \subseteq S\) to be a \(C\)-set (or a \(J\)-set) near zero.