Congruence and dimension of nonseparable metric spaces
HTML articles powered by AMS MathViewer
- by Yasunao Hattori
- Proc. Amer. Math. Soc. 108 (1990), 1103-1105
- DOI: https://doi.org/10.1090/S0002-9939-1990-1000155-8
- PDF | Request permission
Abstract:
In this paper, we prove that, if a metrizable space ${\mathbf {X}}$ has an admissible metric such that ${\mathbf {X}}$ has no two distinct congruent subsets of cardinality 3, then ${\text {ind}}{\mathbf {X}} \leq 1$. We also show that if a non-empty metrizable space ${\mathbf {X}}$ has an admissible star-rigid metric, then ${\text {ind}}{\mathbf {X}} = 0$. The latter answers a question of L. Janos and H. Martin [3].References
- Ludvík Janoš, A metric characterization of zero-dimensional spaces, Proc. Amer. Math. Soc. 31 (1972), 268–270. MR 288739, DOI 10.1090/S0002-9939-1972-0288739-5
- Ludvik Janos, Congruence and one-dimensionality of metric spaces, Proc. Amer. Math. Soc. 103 (1988), no. 4, 1268–1270. MR 955020, DOI 10.1090/S0002-9939-1988-0955020-X
- Ludvik Janos and Harold Martin, Metric characterizations of dimension for separable metric spaces, Proc. Amer. Math. Soc. 70 (1978), no. 2, 209–212. MR 474229, DOI 10.1090/S0002-9939-1978-0474229-9
- Jun-iti Nagata, Modern general topology, 2nd ed., North-Holland Mathematical Library, vol. 33, North-Holland Publishing Co., Amsterdam, 1985. MR 831659
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 108 (1990), 1103-1105
- MSC: Primary 54F45; Secondary 54E35, 54E40
- DOI: https://doi.org/10.1090/S0002-9939-1990-1000155-8
- MathSciNet review: 1000155