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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Connected plane sets which contain no nondegenerate connected simple graph
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by B. D. Garrett PDF
Proc. Amer. Math. Soc. 113 (1991), 451-459 Request permission

Abstract:

Open questions are answered by showing that, if for each vertical line $L$ in the plane, $1 < {k_L} \leq c$ is a cardinal number, there is a connected subset $H$ of the plane such that, if $L$ is a vertical line, then $L \cap H$ has cardinality ${k_L}$ and, if $g$ is a nondegenerate connected subset of $H$, then $g$ contains two points of some vertical line.
References
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 113 (1991), 451-459
  • MSC: Primary 54D05; Secondary 54C60, 54C65
  • DOI: https://doi.org/10.1090/S0002-9939-1991-0991696-9
  • MathSciNet review: 991696