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: Open questions are answered by showing that, if for each vertical line in the plane, is a cardinal number, there is a connected subset of the plane such that, if is a vertical line, then has cardinality and, if is a nondegenerate connected subset of , then contains two points of some vertical line.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-0991696-9

Keywords:
Simple graph,
selection,
connectivity maps

Article copyright:
© Copyright 1991
American Mathematical Society