Density near zero

Let S be a dense subsemigroup of (0;+1). In this pa- per, we state de nition of thick near zero, and also we will introduce a de nition that is equivalent to the de nition of piecewise syndetic near zero which presented by Hindman and Leader in [6]. We de ne density near zero for subsets of S by a collection of nonempty nite subsets of S and we investigate the conditions under these concepts.

Keywords:

The Stone-Cech compacti cation , Density , Piecewise syn- detic set near zero