University of MaraghehSahand Communications in Mathematical Analysis2322-580709120180101Density near zero33432368210.22130/scma.2018.23682ENElham BayatmaneshDepartment of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.Mohammad Akbari TootkaboniDepartment of Mathematics, Faculty of Basic Science, Shahed University, Tehran, Iran.Journal Article20160924Let $S$ 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.http://scma.maragheh.ac.ir/article_23682_545b6075235df500f5ed73aa31024524.pdf