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The number of
subcontinua of the remainder of the plane
Eric Karel van Douwen |
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Vol. 97 (1981), No. 2, 349–355
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Abstract |
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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
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Milestones
Received: 17 September 1980
Published: 1 December 1981
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Authors |
| Eric Karel van Douwen | |
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