Note on cohomological dimension for non-compact spaces

Yukihiro KODAMA

doi:10.2969/jmsj/01840343

Yukihiro KODAMA

著者情報

ジャーナルフリー

1966 年 18 巻 4 号 p. 343-359

DOI https://doi.org/10.2969/jmsj/01840343

詳細

Published: 1966 Received: 1966/02/09 Available on J-STAGE: 2006/09/26 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/09/26 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) R. H. Bing, Metrization of topological spaces, Canad. J. Math., 3 (1951), 175-186.
2) M. Bockstein, On the homological invariants of topological products, I, Trudy Moskov. Mat. Obšc., 5 (1956), 3-80. (Amer. Math. Soc. Transl., Ser. 2, 2 (1959), 173-385.); II, Trudy Moskov. Mat. Obšc., 6 (1957), 3-133.
3) V. Boltyanskii, On dimensional full-valuedness of compacta, Dokl. Akad. Nauk SSSR (N. S.), 67 (1949), 773-776. (Amer. Math. Soc. Transl., Ser. 1, 8 (1951), 6-10.)
4) C. H. Dowker, Mapping theorems for non-compact spaces, Amer. J. Math., 69 (1947), 202-242.
5) C. H. Dowker, Topology of metric complex, Amer. J. Math., 74 (1952), 555-577.
6) C. H. Dowker, On a theorem of Hannor, Ark. Mat., 2 (1954), 307-313.
7) E. Dyer, Regular mappings and dimension, Ann. of Math., 67 (1958), 119-149.
8) E. Dyer, On the dimension of products, Fund. Math., 47 (1959), 141-160.
9) S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton, 1952.
10) O. Hanner, Retraction and extension of mappings of metric and non-metric spaces, Ark. Mat., 2 (1952), 315-360.
11) S. T. Hu, Homotopy theory, Academic Press, New York, 1959.
12) W.Hurewicz and H. Wallman, Dimension theory, Princeton, 1941.
13) I. R. Isbell, Embeddings of inverse limits, Ann. of Math., 70 (1959), 73-84.
14) Y. Kodama, On ANR for metric spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A., 5 (1955), 96-98.
15) Y. Kodama, On a problem of Alexandroff concerning the dimension of product spaces I, J. Math. Soc. Japan, 10 (1958), 380-404; II, J. Math. Soc. Japan., 11 (1959), 94-111.
16) Y. Kodama, Test spaces for homological dimension, Duke Math. J., 29 (1962), 41-50.
17) K. Morita, On the dimension of normal spaces I, Japan. J. Math., 20 (1950), 5-36; II, J. Math. Soc. Japan, 2 (1950), 16-33.
18) K. Morita, On spaces having the weak topology with respect to closed coverings, Proc. Japan Acad., 29 (1953), 537-543; II, Proc. Japan Acad., 30 (1954), 711-717.
19) K. Morita, On the dimension of product spaces, Amer, J. Math., 75 (1953), 205-223.
20) A. Okuyama, On cohomological dimension for paracompact spaces I, Proc. Japan Acad., 38 (1962), 489-494; II, Proc. Japan Acad., 655-659.
21) R. C. O'Neil, The Cech cohomology of paracompact product spaces, Amer. J. Math., 87 (1965), 71-78.
22) F. P. Peterson, Some results on cohomotopy groups, Amer. J. Math., 78 (1956), 243-259.
23) E. G. Skljarenko, On the definition of cohomology dimension, Soviet Math. Dokl., 6 (1965), 478-479.
24) M. Wojdeslawski, Rétracte absolus et hyperspaces des continus, Fund. Math., 32 (1939), 184-192.

Right : 1) R. H. Bing, Metrization of topological spaces, Canad. J. Math., 3 (1951), 175-186.
2) M. Bockstein, On the homological invariants of topological products, I, Trudy Moskov. Mat. Obšc., 5 (1956), 3-80. (Amer. Math. Soc. Transl., Ser. 2, 2 (1959), 173-385.); II, Trudy Moskov. Mat. Obšc., 6 (1957), 3-133.
3) V. Boltyanskii, On dimensional full-valuedness of compacta, Dokl. Akad. Nauk SSSR (N. S.), 67 (1949), 773-776. (Amer. Math. Soc. Transl., Ser. 1, 8 (1951), 6-10.)
4) C. H. Dowker, Mapping theorems for non-compact spaces, Amer. J. Math., 69 (1947), 202-242.
5) C. H. Dowker, Topology of metric complex, Amer. J. Math., 74 (1952), 555-577.
6) C. H. Dowker, On a theorem of Hannor, Ark. Mat., 2 (1954), 307-313.
7) E. Dyer, Regular mappings and dimension, Ann. of Math., 67 (1958), 119-149.
8) E. Dyer, On the dimension of products, Fund. Math., 47 (1959), 141-160.
9) S. Eilenberg and N. Steenrod, Foundations of Algebraic Topology, Princeton, 1952.
10) O. Hanner, Retraction and extension of mappings of metric and non-metric spaces, Ark. Mat., 2 (1952), 315-360.
11) S. T. Hu, Homotopy theory, Academic Press, New York, 1959.
12) W.Hurewicz and H. Wallman, Dimension theory, Princeton, 1941.
13) I. R. Isbell, Embeddings of inverse limits, Ann. of Math., 70 (1959), 73-84.
14) Y. Kodama, On ANR for metric spaces, Sci. Rep. Tokyo Kyoiku Daigaku Sect. A., 5 (1955), 96-98.
15) Y. Kodama, On a problem of Alexandroff concerning the dimension of product spaces I, J. Math. Soc. Japan, 10 (1958), 380-404; II, J. Math. Soc. Japan., 11 (1959), 94-111.
16) Y. Kodama, Test spaces for homological dimension, Duke Math. J., 29 (1962), 41-50.
17) K. Morita, On the dimension of normal spaces I, Japan. J. Math., 20 (1950), 5-36; II, J. Math. Soc. Japan, 2 (1950), 16-33.
18) K. Morita, On spaces having the weak topology with respect to closed coverings, Proc. Japan Acad., 29 (1953), 537-543; II, Proc. Japan Acad., 30 (1954), 711-717.
19) K. Morita, On the dimension of product spaces, Amer, J. Math., 75 (1953), 205-223.
20) A. Okuyama, On cohomological dimension for paracompact spaces I, Proc. Japan Acad., 38 (1962), 489-494; II, Proc. Japan Acad., 655-659.
21) R. C. O'Neil, The Cech cohomology of paracompact product spaces, Amer. J. Math., 87 (1965), 71-78.
22) F. P. Peterson, Some results on cohomotopy groups, Amer, J. Math., 78 (1956), 243-259.
23) E. G. Skljarenko, On the definition of cohomology dimension, Soviet Math. Dokl., 6 (1965), 478-479.
24) M. Wojdeslawski, Rétracte absolus et hyperspaces des continus, Fund. Math., 32 (1939), 184-192.

訂正日: 2006/09/26 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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