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)

 

 

More paracompact box products


Author: Judy Roitman
Journal: Proc. Amer. Math. Soc. 74 (1979), 171-176
MSC: Primary 54B10; Secondary 03E35, 54D20
DOI: https://doi.org/10.1090/S0002-9939-1979-0521893-2
MathSciNet review: 521893
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that if there is no family of cardinality less than c which dominates $ ^\omega \omega $, then the box product of countably many compact first-countable spaces is paracompact; hence the countable box product of compact metrizable spaces is paracompact if $ {2^\omega } = {\omega _2}$. We also give classes of forcing extensions in which many box products are paracompact.


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

  • [A] A. V. Arhangel′skiĭ, The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR 187 (1969), 967–970 (Russian). MR 0251695
  • [vD] E. K. van Douwen, Separation and covering properties of box products and products (to appear).
  • [K] K. Kunen, Box products of compact spaces (to appear).
  • [Ro] Judy Roitman, Paracompact box products in forcing extensions, Fund. Math. 102 (1979), no. 3, 219–228. MR 532956
  • [Ru] Mary Ellen Rudin, The box product of countably many compact metric spaces, General Topology and Appl. 2 (1972), 293–298. MR 0324619
  • [W] S. Williams, Is $ {\square ^\omega }(\omega + 1)$ paracompact? Topology Proceedings 1 (1976).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54B10, 03E35, 54D20

Retrieve articles in all journals with MSC: 54B10, 03E35, 54D20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0521893-2
Article copyright: © Copyright 1979 American Mathematical Society