Certain concepts such as cells, cellular sets, point-like sets, and decomposition spaces are studied and related in normed linear spaces. The relationships between these concepts in general resemble somewhat the corresponding relationships in lîuclidean space. There are certain topological properties in Euclidean ra-space which can be conveniently studied as properties in normed linear spaces. In this paper concepts such as open and closed cells, cellular sets, point-like sets, and

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... spaces are studied and related. Many, but not all, of the relationships between these concepts in infinite-dimensional normed linear spaces resemble the corresponding relationships in finite-dimensional spaces. Throughout the paper, E will denote an arbitrary normed linear space, and 6 will represent the zero element of E. For any positive real number r and any x £ E, let Br(x) = \y £ E: \\x -y|| < r\ and SJ,x) = \y £ E: \\x -y|| = r\. For convenience let Bf = Br(6) and Sf = Sr(d).