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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Connected plane sets which contain no nondegenerate connected simple graph


Author: B. D. Garrett
Journal: Proc. Amer. Math. Soc. 113 (1991), 451-459
MSC: Primary 54D05; Secondary 54C60, 54C65
MathSciNet review: 991696
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Abstract | References | Similar Articles | Additional Information

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-0991696-9
PII: S 0002-9939(1991)0991696-9
Keywords: Simple graph, selection, connectivity maps
Article copyright: © Copyright 1991 American Mathematical Society