Vol. 62, No. 2, 1976

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Vol. 320: 1  2
Online Archive
The Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
Other MSP Journals
On the cardinality relationships between discrete collections and open covers

James Robert Boone

Vol. 62 (1976), No. 2, 359–364

This paper unifies and extends various theorems which deal with the relationship between the cardinality of discrete collections and the cardinality of open coverings. For this purpose, the class of spaces which are irreducible of order α is defined. This class includes the δ𝜃-refinable and the [α,)-refinable spaces. Some examples of applications of this class are: a space is [α,)-compact if and only if it is irreducible of order α and has the α BW property and if X is irreducible of order Δ(X), then Δ(X) L(X) Δ(X)+. The open ordinal space [0,Ω) serves as a model to generate examples of spaces which are irreducible of order α but not irreducible of order β, if β > α.

Mathematical Subject Classification 2000
Primary: 54D20
Secondary: 54F45
Received: 8 May 1975
Revised: 12 November 1975
Published: 1 February 1976
James Robert Boone