Vol. 97, No. 2, 1981

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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