The undecidability of a fundamental problem in cluster set theory

Eidswick, J. A.

doi:10.1090/S0002-9939-1976-0423308-9

The undecidability of a fundamental problem in cluster set theory
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Proc. Amer. Math. Soc. 60 (1976), 116-118 Request permission

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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