  We introduce the notion of smooth cell complexes and its subclass consisting
of gathered cell complexes within the category of diffeological spaces (cf.
Definitions 1 and 3). It is shown that the following hold.
  (1) With respect to the D-topology, every smooth cell complex is a
topological cell complex (cf. Proposition 2). It is paracompact and Hausdorff
if it is countable (cf. Proposition 8).
  (2) Every continuous map between gathered cell complexes is continuously
homotopic to a smooth map (cf. Theorem 5).
  (3) Any topological cell complex is continuously homotopy equivalent to a
gathered (hence smooth) cell complex (cf. Theorem 6).
  (4) Every D-open cover of a smooth countable cell complex has a subordinate
partition of unity by smooth functions (cf. Theorem 9).
