A short proof that a compact ordered space cannot be mapped onto a nonmetric product
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- by W. Bula, W. Dębski and W. Kulpa PDF
- Proc. Amer. Math. Soc. 82 (1981), 312-313 Request permission
Abstract:
In this note we give an elementary proof of a theorem of Treybig: if a product $X \times Y$ of two infinite Hausdorff spaces is a continuous image of a compact linearly ordered space, then $X \times Y$ is metrizable.References
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- R. W. Heath, D. J. Lutzer, and P. L. Zenor, Monotonically normal spaces, Trans. Amer. Math. Soc. 178 (1973), 481–493. MR 372826, DOI 10.1090/S0002-9947-1973-0372826-2
- L. B. Treybig, Concerning continuous images of compact ordered spaces, Proc. Amer. Math. Soc. 15 (1964), 866–871. MR 167953, DOI 10.1090/S0002-9939-1964-0167953-9
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 82 (1981), 312-313
- MSC: Primary 54F05; Secondary 54E35
- DOI: https://doi.org/10.1090/S0002-9939-1981-0609675-3
- MathSciNet review: 609675