TY - JOUR
T1 - WHITNEY APPROXIMATION FOR SMOOTH CW COMPLEX
AU - Iwase, Norio
N1 - Funding Information:
The author thanks the referee for pointing out errors contained in the earlier version of this paper. He also thanks Dan Christensen, Katsuhiko Kuribayashi, Kazuhisa Shimakawa, Tadayuki Haraguchi, and Hiroshi Kihara for their kind and valuable comments and suggestions. More precisely, they pointed out that a CW complex must be smooth around Theorem 9.7, Corollary 9.8 and the entire Section 10 in [II19], and Theorem A.1 in [II19] should be proved rigorously, which is performed in this paper.
Publisher Copyright:
© 2022 Faculty of Mathematics, Kyushu University.
PY - 2022
Y1 - 2022
N2 - We show a Whitney approximation theorem for a continuous map from a manifold to a smooth CW complex, which enables us to show that a topological CW complex is homotopy equivalent to a smooth CW complex in a category of topological spaces. It is also shown that, for any open covering of a smooth CW complex, there exists a partition of unity subordinate to the open covering. In addition, we observe that there are enough many smooth functions on a smooth CW complex.
AB - We show a Whitney approximation theorem for a continuous map from a manifold to a smooth CW complex, which enables us to show that a topological CW complex is homotopy equivalent to a smooth CW complex in a category of topological spaces. It is also shown that, for any open covering of a smooth CW complex, there exists a partition of unity subordinate to the open covering. In addition, we observe that there are enough many smooth functions on a smooth CW complex.
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U2 - 10.2206/kyushujm.76.177
DO - 10.2206/kyushujm.76.177
M3 - Article
AN - SCOPUS:85129002574
SN - 1340-6116
VL - 76
SP - 177
EP - 186
JO - Kyushu Journal of Mathematics
JF - Kyushu Journal of Mathematics
IS - 1
ER -