The Baire category and forcing large Lindelöf spaces with points $G_ \delta$
HTML articles powered by AMS MathViewer
- by Isaac Gorelic
- Proc. Amer. Math. Soc. 118 (1993), 603-607
- DOI: https://doi.org/10.1090/S0002-9939-1993-1132417-0
- PDF | Request permission
Abstract:
For $\kappa$ as large an aleph as we want, we construct by forcing a model in which CH holds and there is a Lindelöf zero-dimensional space of size $\kappa$ with points ${G_\delta }$.References
- P. S. Alexandroff and P. S. Urysohn, Memoire sur les espaces topologiques compacts, Nederl. Akad. Wetensch. Proc. Ser. A 14 (1929), 1-96.
A. V. Arhangelâskii, On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl. 10 (1969), 951-955.
- Saharon Shelah, On some problems in general topology, Set theory (Boise, ID, 1992â1994) Contemp. Math., vol. 192, Amer. Math. Soc., Providence, RI, 1996, pp. 91â101. MR 1367138, DOI 10.1090/conm/192/02352
- I. JuhĂĄsz, Cardinal functions. II, Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 63â109. MR 776621
- A. Dow, Two applications of reflection and forcing to topology, General topology and its relations to modern analysis and algebra, VI (Prague, 1986) Res. Exp. Math., vol. 16, Heldermann, Berlin, 1988, pp. 155â172. MR 952602
- Murray Bell and John Ginsburg, First countable Lindelöf extensions of uncountable discrete spaces, Canad. Math. Bull. 23 (1980), no. 4, 397â399. MR 602591, DOI 10.4153/CMB-1980-058-6
Bibliographic Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 603-607
- MSC: Primary 03E35; Secondary 03E50, 54A25, 54A35
- DOI: https://doi.org/10.1090/S0002-9939-1993-1132417-0
- MathSciNet review: 1132417