C-embedding, Lindel¨ofness, and ˇCech-completeness
Keywords:
C-embedding, Lindelöf, Čech-complete, product, perfect preimageAbstract
We show that in the class of Lindelöf Čech-complete spaces the property of being C-embedded is quite well-behaved. It admits a useful characterization that can be used to show that products and perfect preimages of C-embedded spaces are again C-embedded. We also show that both properties, Lindelöf and Čech-complete, are needed in the product result.
References
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Alan Dow, Klaas Pieter Hart, Jan van Mill, and Hans Vermeer, Some realcompact spaces, Topology Proceedings 62 (2023), 205–216. E-published on August 25, 2023. MR4634391
Alan Dow, Klaas Pieter Hart, Jan van Mill, and Hans Vermeer , Closed copies of N in Rω1 , posted on 31 October, 2023, DOI 10.48550/arXiv.2307.07223. arXiv:2307.07223 [math.GN].
Ryszard Engelking, General Topology, 2nd ed., Sigma Series in Pure Mathematics, vol. 6, Heldermann Verlag, Berlin, 1989. Translated from the Polish by the author. MR1039321
Leonard Gillman and Meyer Jerison, Rings of continuous functions, Graduate Texts in Mathematics, No. 43, Springer-Verlag, New York-Heidelberg, 1976. Reprint of the 1960 edition. MR0407579
Gary Gruenhage, The Sorgenfrey line is not an elastic space, Proc. Amer. Math. Soc. 38 (1973), 665–666, DOI 10.2307/2038973. MR0317286
M. Henriksen, J. R. Isbell, and D. G. Johnson, Residue class fields of lattice-ordered algebras, Fund. Math. 50 (1961/62), 107–117, DOI 10.4064/fm-50-2-107-117. MR0133350
Jan Menu, A partition of R in two homogeneous and homeomorphic parts, Abstracta. 5th Winter School on Abstract Analysis (Zdeněk Frolík, ed.), Czechoslovak Academy of Sciences, Praha, 1977, pp. 43–49.
Jan van Mill, Homogeneous subsets of the real line, Compositio Math. 46 (1982), no. 1, 3–13. MR0660152
Colloquium co-topology: 1964–1965, Mathematical Centre, Stichting Mathematisch Centrum, Amsterdam, 1965. Notes by J. M. Aarts; Introduction by J. de Groot. MR0261539
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Published
2025-04-30
How to Cite
Dow, A., Hart, K. P., Van Mill, J., & Vermeer, H. (2025). C-embedding, Lindel¨ofness, and ˇCech-completeness. Topology Proceedings, 67, 1–12. Retrieved from https://topology.journals.yorku.ca/index.php/tp/article/view/17
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Section
General and Set Theoretic Topology (Research Papers)
