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Transactions of the American Mathematical Society

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A study of metric-dependent dimension functions


Authors: Keiô Nagami and J. H. Roberts
Journal: Trans. Amer. Math. Soc. 129 (1967), 414-435
MSC: Primary 54.70
DOI: https://doi.org/10.1090/S0002-9947-1967-0215289-7
MathSciNet review: 0215289
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  • [1] P. Alexandroff, On some results in the theory of topological spaces obtained during the last twenty five years, Uspehi Mat. Nauk 15 (1960), 25-95. MR 0119181 (22:9947)
  • [2] C. H. Dowker and W. Hurewicz, Dimensions of metric spaces, Fund. Math. 43 (1956), 83-87. MR 0079250 (18:56g)
  • [3] S. Eilenberg and E. Otto, Quelques propriétés caracteristiques de la dimension, Fund. Math. 31 (1938), 149-153.
  • [4] O. Hanner, Retraction and extension of mappings of metric and nonmetric spaces, Ark. Mat. 2 (1952), 315-360. MR 0050875 (14:396b)
  • [5] E. Hemmingsen, Some theorems in dimension theory for normal Hausdorff spaces, Duke Math. J. 13 (1946), 495-504. MR 0018819 (8:334e)
  • [6] J. G. Hocking and G. S. Young, Topology, Addison-Wesley, Reading, Mass., 1961. MR 0125557 (23:A2857)
  • [7] W. Hurewicz and H. Wallman, Dimension theory, Princeton Univ. Press, Princeton, N. J., 1941. MR 0006493 (3:312b)
  • [8] M. Katětov, On the relations between the metric and topological dimensions, Czechoslovak Math. J. 8 (1958), 163-166. MR 0105084 (21:3830)
  • [9] R. L. Moore, Foundations of point set theory, Amer. Math. Soc. Colloq. Publ., Vol. 13, Amer. Math. Soc., Providence, R. I., 1932. MR 0150722 (27:709)
  • [10] K. Morita, On the dimension of normal spaces. I, Japan. J. Math. 20 (1950), 5-36. MR 0045374 (13:573c)
  • [11] -, On the dimension of normal spaces. II, J. Math. Soc. Japan 2 (1950), 16-33. MR 0039990 (12:627c)
  • [12] -, Normal families and dimension theory for metric spaces, Math. Ann. 128 (1954), 350-362. MR 0065906 (16:501h)
  • [13] K. Nagami, Mappings of finite order and dimension theory, Japan. J. Math. 30 (1960), 25-54. MR 0142101 (25:5494)
  • [14] -, Note on metrizability and n-dimensionality, Proc. Japan Acad. 36 (1960), 565-570. MR 0133104 (24:A2938)
  • [15] K. Nagami and J. H. Roberts, Metric-dependent dimension functions, Proc. Amer. Math. Soc. 16 (1965), 601-604. MR 0195059 (33:3264)
  • [16] -, A note on countable-dimensional metric spaces, Proc. Japan Acad. 41 (1965), 155-158. MR 0187204 (32:4658)
  • [17] J. Nagata, Note on dimension theory for metric spaces, Fund. Math. 45 (1958), 143-181. MR 0105081 (21:3827)
  • [18] -, On a special metric and dimension, Fund. Math. 55 (1964), 181-194. MR 0180956 (31:5186)
  • [19] K. Sitnikov, An example of a 2-dimensional set in the 3-dimensional Euclidean space, which allows a deformation as small as desired in a 1-dimensional polyhedron, and some new character of the dimension of the sets in Euclidean spaces, Dokl. Akad. Nauk SSSR 66 (1949), 1059-1062. MR 0030747 (11:45d)
  • [20] -, On the dimension of nonclosed sets of Euclidean space, Dokl. Akad. Nauk SSSR 83 (1952), 31-34. MR 0047327 (13:860d)
  • [21] A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977-982. MR 0026802 (10:204c)
  • [22] P. Vopěnka, Remarks on the dimension of metric spaces, Czechoslovak Math. J. 9 (1959), 519-522. MR 0111017 (22:1884)

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DOI: https://doi.org/10.1090/S0002-9947-1967-0215289-7
Article copyright: © Copyright 1967 American Mathematical Society

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