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 density character of function spaces


Author: N. Noble
Journal: Proc. Amer. Math. Soc. 42 (1974), 228-233
MSC: Primary 54C35
DOI: https://doi.org/10.1090/S0002-9939-1974-0328855-4
MathSciNet review: 0328855
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For topologies between the pointwise topology and the compact-open topology, the density character of $ C(X)$ (and, for certain spaces $ Z,C(X,Z)$) is described in terms of a cardinal invariant of X. The Hewitt-Pondiczery theorem on the density character of product spaces follows as a corollary.


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

  • [1] W. Comfort and A. Hager, Dense subspaces of some spaces of continuous functions, Math. Z. 114 (1970), 373-389. MR 0410646 (53:14394)
  • [2] E. Hewitt, A remark on density characters, Bull. Amer. Math. Soc. 52 (1946), 641-643. MR 8, 139. MR 0017329 (8:139f)
  • [3] E. S. Pondiczery, Power problems in abstract spaces, Duke Math. J. 11 (1944), 835-837. MR 6, 119. MR 0011104 (6:119g)
  • [4] V. Saks and R. M. Stephenson, Jr., Products of $ \mathfrak{M}$-compact spaces, Proc. Amer. Math. Soc. 28 (1971), 279-288. MR 42 #8448. MR 0273570 (42:8448)
  • [5] Yu. M. Smirnov, On the weight of the ring of bounded continuous functions over a normal space, Mat. Sb. 30(72) (1952), 213-218. (Russian) MR 14, 70. MR 0048789 (14:70b)
  • [6] G. Vidossich, Characterizing separability of function spaces, Invent. Math. 10 (1970), 205-208. MR 42 #2424. MR 0267522 (42:2424)
  • [7] S. Willard, General topology, Addison-Wesley, Reading, Mass., 1970. MR 41 #9173. MR 0264581 (41:9173)

Similar Articles

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

Retrieve articles in all journals with MSC: 54C35


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0328855-4
Keywords: Density character, separable spaces, function spaces
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society