Proper mappings and dimension
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- by James Keesling PDF
- Proc. Amer. Math. Soc. 29 (1971), 202-204 Request permission
Abstract:
In this note it is shown that if W is the long line and f is a proper mapping of $W \times [0,1]$ into Y, then $\dim Y \geqq 2$. This answers a question raised by Isbell.References
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- J. R. Isbell, Uniform spaces, Mathematical Surveys, No. 12, American Mathematical Society, Providence, R.I., 1964. MR 0170323
- K. Kuratowski, Topology. Vol. II, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe [Polish Scientific Publishers], Warsaw, 1968. New edition, revised and augmented; Translated from the French by A. Kirkor. MR 0259835 A. Lelek, Some problems in metric topology, Mimeographed Lecture Notes, Louisiana State University, Baton Rouge, La., 1965/66. J. Nagata, Modern dimension theory, Bibliotheca Math., vol. 6, Interscience, New York, 1965. MR 34 #8380.
- A. H. Stone, Metrizability of decomposition spaces, Proc. Amer. Math. Soc. 7 (1956), 690–700. MR 87078, DOI 10.1090/S0002-9939-1956-0087078-6
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 202-204
- MSC: Primary 54.70
- DOI: https://doi.org/10.1090/S0002-9939-1971-0286085-6
- MathSciNet review: 0286085