Document Type: Research Paper

**Authors**

Department of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.

**Abstract**

Let $S$ be a dense subsemigroup of $(0,+\infty)$. In this paper, we state definition of thick near zero, and also we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman and Leader in [6]. We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions under these concepts.

**Keywords**

**Main Subjects**

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