A Closed Manifold Is a Fat Cw Complex

The main purpose of this paper is to introduce a new smooth version of a CW complex named a fat CW complex, and to show that it includes all closed manifolds, because existing smooth versions of CW complexes, e.g., that of Iwase (Kyushu J. Math.76(1) (2022), 177-186), do not have such a property.We also verify that the de Rham theorem holds for a fat CW complex and that a regular CW complex is reflexive in the sense of Batubenge, Iglesias-Zemmour, Karshon, and Watts (Rocky Mountain J. Math.To appear).Further, any topological CW complex is topologically homotopy equivalent to a fat CW complex.So, a fat CW complex enjoys many nice properties.