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Proceedings of the American Mathematical Society

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

 

 

The undecidability of a fundamental problem in cluster set theory


Author: J. A. Eidswick
Journal: Proc. Amer. Math. Soc. 60 (1976), 116-118
MSC: Primary 54E30; Secondary 04A15
DOI: https://doi.org/10.1090/S0002-9939-1976-0423308-9
MathSciNet review: 0423308
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Abstract: The undecidability of the existence of a nonmetrizable normal picket fence space is established and used to establish the undecidability of the following statement: Any family of approach curves (approaching a point in $ {{\mathbf{R}}^2}$) along which cluster sets can be arbitrarily preassigned has a nonintersecting truncation.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0423308-9
Keywords: Cluster sets, approach curves, Moore spaces, picket fence spaces, metrizability, infinite derivatives
Article copyright: © Copyright 1976 American Mathematical Society