Mappings defined on 0-dimensional spaces and dimension theory

Keiô NAGAMI

doi:10.2969/jmsj/01410101

Keiô NAGAMI

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1962 Volume 14 Issue 1 Pages 101-118

DOI https://doi.org/10.2969/jmsj/01410101

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Published: 1962 Received: July 24, 1961 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : Keio NAGAMI¹⁾
Right : Keiô NAGAMI¹⁾

Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) P. Alexandroff, On some results in the theory of topological spaces obtained during the last twenty five years, Uspehi Mat. Nauk USSR, 15 (92) (1960), 25-95.
2) P. Alexandroff-H. Hopf, Topologie I, 1935.
3) C. H. Dowker, Inductive dimension of completely normal spaces, Quart. J. Math. Oxford, 4 (1953), 267-281.
4) W. Hurewicz, Ein Theorem der Dimensionstheorie, Ann. Math., 31(1930), 176-180.
5) M. Katetov, On the dimension of non-separable spaces I, Cechoslovack Math. J., 2 (77) (1952), 333-368.
6) C. Kuratowski, Sur l'application des espaces fonctionnels à la théorie de la dimension, Fund. Math., 18 (1932), 285-292.
7) C. Kuratowski, Topologie II, 1950.
8) O. Lokutsievski, On the dimension of compact spaces, Dokl. Acad. Nauk USSR, 67 (1949), 217-219.
9) A. Lunz, A compact space, the inductive dimension of which is greater than the dimension defined by coverings, Dokl. Acad. Nauk USSR, 66 (1946), 801-803.
10) E. Michael, Another note on paracompact spaces, Proc. Amer. Math. Soc., 8 (1957), 822-828.
11) H. Miyazaki, The paracompactness of CW-complexes, Tohoku Math. J., 4 (1952), 309-313.
12) K. Morita, Normal families and dimension theory for metric spaces, Math. Ann., 128 (1954), 350-362.
13) K. Morita, On closed mappings and dimension, Proc. Japan Acad., 32 (1956), 161-165.
14) K. Morita, A condition for the metrizability of topological spaces and for n-dimensionality, Sci. Rep. Tokyo Kyoiku Daigaku sec. A, 5 (1955), 33-36.
15) K. Morita, On spaces having the weak topology with respect to closed coverings, Proc. Japan Acad., 29 (1953), 537-543.
16) K. Nagami, Finite-to-one closed mappings and dimension IV, Proc. Japan Acad., 37 (1961), 193-195.
17) K. Nagami, Mappings of finite order and dimension theory, Jap. J. Math., 30 (1960), 25-54.
18) K. Nagami, A note on Hausdorff spaces with the star-finite property I, Proc. Japan Acad., 37 (1961), 131-134.
19) K. Nagami, A note on Hausdorff spaces with the star-finite property II, Proc. Japan Acad., 37 (1961), 189-192.
20) J. Nagata, A generalization of a theorem of W. Hurewicz, J. Inst. Polytech. Osaka City Univ., 9 (1958), 37-38.
21) B. A. Pasynkov, On polyhedral spectra and dimension of compact spaces, especially of compact groups, Dokl. Acad. Nauk USSR, 121 (1958), 45-48.
22) B. A. Pasynkov, On the coincidence of different definitions of the dimension for the locally compact groups, Dokl. Acad. Nauk USSR, 132 (1960), 1035-1037.
23) P. Vopenka, On the dimension of compact spaces, Cechoslovack Math. J., 8 (83) (1958), 319-327.
24) J.H.C. Whitehead, Combinatorial homotopy I, Bull. Amer. Math. Soc., 55 (1949), 213-245.

Right : [1] P. Alexandroff, On some results in the theory of topological spaces obtained during the last twenty five years, Uspehi Mat. Nauk USSR, 15 (92) (1960), 25-95.
[2] P. Alexandroff-H. Hopf, Topologie I, 1935.
[3] C. H. Dowker, Inductive dimension of completely normal spaces, Quart. J. Math. Oxford, 4 (1953), 267-281.
[4] W. Hurewicz, Ein Theorem der Dimensionstheorie, Ann. Math., 31 (1930), 176-180.
[5] M. Katetov, On the dimension of non-separable spaces I, Cechoslovack Math. J., 2 (77) (1952), 333-368.
[6] C. Kuratowski, Sur l'application des espaces fonctionnels à la théorie de la dimension, Fund. Math., 18 (1932), 285-292.
[7] C. Kuratowski, Topologie II, 1950.
[8] O. Lokutsievski, On the dimension of compact spaces, Dokl. Acad. Nauk USSR, 67 (1949), 217-219.
[9] A. Lunz, A compact space, the inductive dimension of which is greater than the dimension defined by coverings, Dokl. Acad. Nauk USSR, 66 (1946), 801-803.
[10] E. Michael, Another note on paracompact spaces, Proc. Amer. Math. Soc., 8 (1957), 822-828.
[11] H. Miyazaki, The paracompactness of CW-complexes, Tôhoku Math. J., 4 (1952), 309-313.
[12] K. Morita, Normal families and dimension theory for metric spaces, Math. Ann., 128 (1954), 350-362.
[13] K. Morita, On closed mappings and dimension, Proc. Japan Acad., 32 (1956), 161-165.
[14] K. Morita, A condition for the metrizability of topological spaces and for n-dimensionality, Sci. Rep. Tokyo Kyoiku Daigaku sec. A, 5 (1955), 33-36.
[15] K. Morita, On spaces having the weak topology with respect to closed coverings, Proc. Japan Acad., 29 (1953), 537-543.
[16] K. Nagami, Finite-to-one closed mappings and dimension IV, Proc. Japan Acad., 37 (1961), 193-195.
[17] K. Nagami, Mappings of finite order and dimension theory, Jap. J. Math., 30 (1960), 25-54.
[18] K. Nagami, A note on Hausdorff spaces with the star-finite property I, Proc. Japan Acad., 37 (1961), 131-134.
[19] K. Nagami, A note on Hausdorff spaces with the star-finite property II, Proc. Japan Acad., 37 (1961), 189-192.
[20] J. Nagata, A generalization of a theorem of W. Hurewicz, J. Inst. Polytech. Osaka City Univ., 9 (1958), 37-38.
[21] B. A. Pasynkov, On polyhedral spectra and dimension of compact spaces, especially of compact groups, Dokl. Acad. Nauk USSR, 121 (1958), 45-48.
[22] B. A. Pasynkov, On the coincidence of different definitions of the dimension for the locally compact groups, Dokl. Acad. Nauk USSR, 132 (1960), 1035-1037.
[23] P. Vopenka, On the dimension of compact spaces, Cechoslovack Math. J., 8 (83) (1958), 319-327.
[24] J. H. C. Whitehead, Combinatorial homotopy I, Bull. Amer. Math. Soc., 55 (1949), 213-245.

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