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)

 
 

 

Property C and function spaces


Author: Masami Sakai
Journal: Proc. Amer. Math. Soc. 104 (1988), 917-919
MSC: Primary 54A25; Secondary 54C35, 54D20
DOI: https://doi.org/10.1090/S0002-9939-1988-0964873-0
MathSciNet review: 964873
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For a Tychonoff space $ X$, we show that each finite product of $ X$ has property $ {\text{C''}}$ iff $ {C_p}\left( X \right)$ has countable strong fan tightness, where $ {C_p}\left( X \right)$ is the function space on $ X$ with the topology of pointwise convergence.


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

  • [1] A. V. Arkhangel'skii, Hurewicz spaces, analytic sets, and fan tightness of function spaces, Soviet Math. Dokl. 33 (1986), 396-399. MR 837289 (87i:54079)
  • [2] -, Structure and classification of topological spaces and cardinal invariants, Russian Math. Surveys 33 (1978), 33-96. MR 526012 (80i:54005)
  • [3] R. Engelking, General topology, PWN, Warsaw, 1977. MR 0500780 (58:18316b)
  • [4] J. Gerlits, Some properties of $ C\left( X \right)$. II, Topology Appl. 15 (1983), 255-262. MR 694545 (84i:54018)
  • [5] J. Gerlits, and Zs. Nagy, Some properties of $ C\left( X \right)$. I, Topology Appl. 14 (1982), 151-161. MR 667661 (84f:54021)
  • [6] C. Kuratowski, Topology, Vol. 1, Academic Press, New York, 1966.
  • [7] R. Laver, On the consistency of Borel's conjecture, Acta Math. 137 (1976), 151-169. MR 0422027 (54:10019)
  • [8] A. Lelek, Some cover properties of spaces, Fund. Math. 64 (1969), 209-218. MR 0242108 (39:3442)
  • [9] F. Rothberger, Eine Verschärfung der Eigenschaft $ C$, Fund. Math. 30 (1938), 50-55.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54A25, 54C35, 54D20

Retrieve articles in all journals with MSC: 54A25, 54C35, 54D20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0964873-0
Keywords: Function space, property $ {\text{C''}}$
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society