More paracompact box products
HTML articles powered by AMS MathViewer
- by Judy Roitman PDF
- Proc. Amer. Math. Soc. 74 (1979), 171-176 Request permission
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
- A. V. Arhangel′skiĭ, The power of bicompacta with first axiom of countability, Dokl. Akad. Nauk SSSR 187 (1969), 967–970 (Russian). MR 0251695 E. K. van Douwen, Separation and covering properties of box products and products (to appear). K. Kunen, Box products of compact spaces (to appear).
- Judy Roitman, Paracompact box products in forcing extensions, Fund. Math. 102 (1979), no. 3, 219–228. MR 532956, DOI 10.4064/fm-102-3-219-228
- Mary Ellen Rudin, The box product of countably many compact metric spaces, General Topology and Appl. 2 (1972), 293–298. MR 324619 S. Williams, Is ${\square ^\omega }(\omega + 1)$ paracompact? Topology Proceedings 1 (1976).
Additional Information
- © Copyright 1979 American Mathematical Society
- 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