Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The character of $ \omega \sb{1}$ in first countable spaces

Author: William G. Fleissner
Journal: Proc. Amer. Math. Soc. 62 (1977), 149-155
MSC: Primary 54A25; Secondary 04A20
MathSciNet review: 0438272
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We define a cardinal function $ \chi (P,Q)$, where P and Q are properties of topological spaces. We show that it is consistent and independent that $ \chi ({\omega _1},\;{\text{first}}\;{\text{countable}}) = {\omega _1}$.

References [Enhancements On Off] (What's this?)

  • [D] Keith J. Devlin, Aspects of constructibility, Lecture Notes in Mathematics, Vol. 354, Springer-Verlag, Berlin-New York, 1973. MR 0376351
  • [D'] Keith J. Devlin, Kurepa’s hypothesis and the continuum, Fund. Math. 89 (1975), no. 1, 23–31. MR 0398826
  • [F] William Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), 294–298. MR 0362240, 10.1090/S0002-9939-1974-0362240-4
  • [F'] William G. Fleissner, A normal collectionwise Hausdorff, not collectionwise normal space, General Topology and Appl. 6 (1976), no. 1, 57–64. MR 0391032
  • [H] Stephen H. Hechler, On the existence of certain cofinal subsets of ^{𝜔}𝜔, Axiomatic set theory (Proc. Sympos. Pure Math., Vol. XIII, Part II, Univ. California, Los Angeles, Calif., 1967) Amer. Math. Soc., Providence, R.I., 1974, pp. 155–173. MR 0360266
  • [J] Thomas J. Jech, Trees, J. Symbolic Logic 36 (1971), 1–14. MR 0284331
  • [Ju] I. Juhász, Consistency results in topology, Logic Handbook (to appear).
  • [JW] I. Juhász and William Weiss, On a problem of Sikorski, Fund. Math. 100 (1978), no. 3, 223–227. MR 509548
  • [M] William Mitchell, Aronszajn trees and the independence of the transfer property, Ann. Math. Logic 5 (1972/73), 21–46. MR 0313057
  • [R] Mary Ellen Rudin, Lectures on set theoretic topology, Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, R.I., 1975. Expository lectures from the CBMS Regional Conference held at the University of Wyoming, Laramie, Wyo., August 12–16, 1974; Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 23. MR 0367886
  • [Sh] S. Shelah, Decomposing uncountable squares into countably many chains (to appear).
  • [S] J. H. Silver, The independence of Kurepa's conjecture and two-cardinal conjectures in model theory, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 383-390. MR 43 #3112.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54A25, 04A20

Retrieve articles in all journals with MSC: 54A25, 04A20

Additional Information

Keywords: Cardinal functions in topology, diamond plus, Kurepa's hypothesis
Article copyright: © Copyright 1977 American Mathematical Society