A study of metric-dependent dimension functions

Nagami, Keiô; Roberts, J. H.

doi:10.1090/S0002-9947-1967-0215289-7

A study of metric-dependent dimension functions
HTML articles powered by AMS MathViewer

by Keiô Nagami and J. H. Roberts

Trans. Amer. Math. Soc. 129 (1967), 414-435

DOI: https://doi.org/10.1090/S0002-9947-1967-0215289-7

PDF | Request permission

References

P. S. Aleksandrov, Some results in the theory of topological spaces obtained within the last twenty-five years, Russian Math. Surveys 15 (1960), no. 2, 23–83. MR 0119181, DOI 10.1070/RM1960v015n02ABEH004216
C. H. Dowker and W. Hurewicz, Dimension of metric spaces, Fund. Math. 43 (1956), 83–88. MR 79250, DOI 10.4064/fm-43-1-83-88

Quelques propriétés caracteristiques de la dimension

31

Olof Hanner, Retraction and extension of mappings of metric and non-metric spaces, Ark. Mat. 2 (1952), 315–360. MR 50875, DOI 10.1007/BF02591501
Erik Hemmingsen, Some theorems in dimension theory for normal Hausdorff spaces, Duke Math. J. 13 (1946), 495–504. MR 18819
John G. Hocking and Gail S. Young, Topology, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961. MR 0125557
Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
Miroslav Katětov, On the relation between the metric and topological dimension, Czechoslovak Math. J. 8(83) (1958), 163–166 (Russian, with English summary). MR 105084
R. L. Moore, Foundations of point set theory, Revised edition, American Mathematical Society Colloquium Publications, Vol. XIII, American Mathematical Society, Providence, R.I., 1962. MR 0150722
Kiichi Morita, On the dimension of normal spaces. I, Jpn. J. Math. 20 (1950), 5–36. MR 45374, DOI 10.4099/jjm1924.20.0_{5}
Kiiti Morita, On the dimension of normal spaces. II, J. Math. Soc. Japan 2 (1950), 16–33. MR 39990, DOI 10.2969/jmsj/00210016
Kiiti Morita, Normal families and dimension theory for metric spaces, Math. Ann. 128 (1954), 350–362. MR 65906, DOI 10.1007/BF01360142
Keiô Nagami, Mappings of finite order and dimension theory, Jpn. J. Math. 30 (1960), 25–54. MR 142101, DOI 10.4099/jjm1924.30.0_{2}5
Keiô Nagami, Note on metrizability and $n$-dimensionality, Proc. Japan Acad. 36 (1960), 565–570. MR 133104
K. Nagami and J. H. Roberts, Metric-dependent dimension functions, Proc. Amer. Math. Soc. 16 (1965), 601–604. MR 195059, DOI 10.1090/S0002-9939-1965-0195059-2
Keiô Nagami and J. H. Roberts, A note on countable-dimensional metric spaces, Proc. Japan Acad. 41 (1965), 155–158. MR 187204
J. Nagata, Note on dimension theory for metric spaces, Fund. Math. 45 (1958), 143–181. MR 105081, DOI 10.4064/fm-45-1-143-181
J. Nagata, On a special metric and dimension, Fund. Math. 55 (1964), 181–194. MR 180956, DOI 10.4064/fm-55-2-181-194
K. Sitnikov, The definition of the dimension of a closed set by a metric property of the complementary space, Doklady Akad. Nauk SSSR (N.S.) 66 (1949), 1059–1062 (Russian). MR 0030747
K. Sitnikov, On the dimension of non-closed sets of Euclidean space, Doklady Akad. Nauk SSSR (N.S.) 83 (1952), 31–34 (Russian). MR 0047327
A. H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948), 977–982. MR 26802, DOI 10.1090/S0002-9904-1948-09118-2
Petr Vopěnka, Remark on the dimension of metric spaces, Czechoslovak Math. J. 9(84) (1959), 519–522 (Russian, with English summary). MR 111017