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Proceedings of the American Mathematical Society

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



Rigid pairs of long arcs

Author: Gary G. Miller
Journal: Proc. Amer. Math. Soc. 31 (1972), 591-594
MathSciNet review: 0290336
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Abstract: Arcs (linearly ordered continua) $ A$ and $ B$ are constructed such that every map from $ A$ to $ B$ and every map from $ B$ to $ A$ is constant. The Generalized Continuum Hypothesis is sufficient for the existence of two such arcs each of cardinality $ {2^\aleph }$ for each uncountable cardinal $ \aleph $.

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Keywords: Arcs, linearly ordered continua, continuous functions, Urysohn's lemma, lexicographic product, ordinal power, rigid pairs of spaces
Article copyright: © Copyright 1972 American Mathematical Society

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