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Pairwise disjoint eight‐shaped curves in hybrid planes
Author(s) -
Costantini Camillo
Publication year - 2007
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200710003
Subject(s) - disjoint sets , mathematics , pairwise comparison , countable set , combinatorics , line (geometry) , plane (geometry) , real line , parallels , geometry , statistics , mechanical engineering , engineering
We introduce a suitable notion of eight‐shaped curve in the product S × ℝ of a Suslin line S for the real line ℝ, and we prove that if S is dense in itself, then every collection of pairwise disjoint eight‐shaped curves in S × ℝ is countable. This parallels a folklore result which holds for the real plane. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)