Vol. 97, No. 2, 1981

Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 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
The number of subcontinua of the remainder of the plane

Eric Karel van Douwen

Vol. 97 (1981), No. 2, 349–355

Denote the Euclidean plane by Π, and for a completely regular space X denote its remainder βX X by X. We will prove that Π has 2c pairwise nonhomeomorphic subcontinua by finding a family 𝒳 of nondegenerate subcontinua each of which has a unique cut point, and then finding 2c members of 𝒳 which are pairwise nonhomeomorphic because their cut points behave differently. It is of interest that the second part uses a method of Frolík originally invented to prove that X is not homogeneous for nonpseudocompact X.

Mathematical Subject Classification 2000
Primary: 54D40
Secondary: 54F15
Received: 17 September 1980
Published: 1 December 1981
Eric Karel van Douwen