Open images of orderable spaces
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- by M. Hušek and W. Kulpa PDF
- Proc. Amer. Math. Soc. 88 (1983), 711-715 Request permission
Abstract:
The class of open continuous images of orderable spaces is characterized, and it is shown that it contains all suborderable spaces. Several results concerning open images of metrizable spaces are generalized to higher cardinals, e.g., every completely linearly uniformizable space is an open continuous image of a Baire space ${({\kappa ^\lambda })_\lambda }$.References
- W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Die Grundlehren der mathematischen Wissenschaften, Band 211, Springer-Verlag, New York-Heidelberg, 1974. MR 0396267, DOI 10.1007/978-3-642-65780-1
- Eduard Čech, Topological spaces, Publishing House of the Czechoslovak Academy of Sciences, Prague; Interscience Publishers John Wiley & Sons, London-New York-Sydney, 1966. Revised edition by Zdeněk Frolík and Miroslav Katětov; Scientific editor, Vlastimil Pták; Editor of the English translation, Charles O. Junge. MR 0211373
- Ryszard Engelking, Topologia ogólna, Państwowe Wydawnictwo Naukowe, Warsaw, 1975 (Polish). Biblioteka Matematyczna, Tom 47. [Mathematics Library. Vol. 47]. MR 0500779
- R. Frankiewicz and W. Kulpa, On order topology of spaces having uniform linearly ordered bases, Comment. Math. Univ. Carolin. 20 (1979), no. 1, 37–41. MR 526146 F. Hausdorff, Über innere Abbildungen, Fund. Math. 23 (1934), 279-291. M. Hušek, Linearly uniformizable spaces, Rapport Wisk. Sem. Vrije Univ. 119 (1980), 19 pp.
- Đuro Kurepa, On the existence of pseudometric non totally orderable spaces, Glasnik Mat.-Fiz. Astronom. Društvo Mat. Fiz. Hrvatske Ser. II 18 (1963), 183–194 (English, with Serbo-Croatian summary). MR 172235
- Đuro Kurepa, Sur l’écart abstrait, Glasnik Mat.-Fiz. Astronom. Društvo Mat. Fiz. Hrvatske Ser. II 11 (1956), 105–134 (French, with Serbo-Croatian summary). MR 102789
- E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J. 26 (1959), 647–651. MR 109343, DOI 10.1215/S0012-7094-59-02662-6
- V. Ponomarev, Axioms of countability and continuous mappings, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 8 (1960), 127–134 (Russian, with English summary). MR 0116314
- J. M. van Wouwe, GO-spaces and generalizations of metrizability, Mathematical Centre Tracts, vol. 104, Mathematisch Centrum, Amsterdam, 1979. MR 541832
Additional Information
- © Copyright 1983 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 88 (1983), 711-715
- MSC: Primary 54C10; Secondary 06F30, 54F05
- DOI: https://doi.org/10.1090/S0002-9939-1983-0702305-3
- MathSciNet review: 702305