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Two More Hereditarily Separable Non-Lindelöf Spaces

  • I. Juhász (a1), K. Kunen (a1) and M. E. Rudin (a1)

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Our method using CH is a blend of two earlier constructions (Hajnal-Juhász [2] and Ostaszewski [4]) of hereditarily separable (HS), regular, non-Lindelöf, first countable spaces. [4] produces a much better space than ours in § 1 ; it has all of our properties except that it is not realcompact (which is probably more interesting), and it is countably compact as well; however, the construction works only under ◇, which implies the continuum hypothesis (CH) but is not equivalent to it.

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References

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1. Hajnal, A. and I. Juhâsz, On hereditarily a-Lindelof and a-separable spaces, Ann. Univ. Sc. Budapest 11 (1968), 115124.
2. On first countable non-Lindelôf S-spaces, preprint 57 (1973) of Math. Inst. Hungarian Acad. Sci.
3. Hodel, R., On a theorem of Arhangelskii concerningLindelôf p-spaces, Can. J. Math. 27 (1975), 450468.
4. Ostaszewski, A., On countably compact, perfectly normal spaces, J. London Math. Soc. (to appear).
5. Pfeffer, W. F., On the regularity of Borel measures, Math. Colloq. U.C.T. 7 (1973), 125142.
6. Rudin, M. E., A hereditarily separable Dowker space, Symposia Math. (March 1973), Published by Institute Nazionale di Alta Math., Rome.
7. Rudin, M. E., A normal space X such that XXI is not normal, Fund. Math. 78 (1971-72), 179186.
8. Gillman, L. and Jerison, M., Rings of continuous functions (D. van Nostrand, Princeton, N.J. 1960), Corollary 8.18, p. 122.
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Canadian Journal of Mathematics
  • ISSN: 0008-414X
  • EISSN: 1496-4279
  • URL: /core/journals/canadian-journal-of-mathematics
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