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Can a $ 2$-coherent Peano continuum separate $ E\sp{3}$?

Author: W. C. Chewning
Journal: Proc. Amer. Math. Soc. 30 (1971), 185-188
MSC: Primary 54.55
MathSciNet review: 0288733
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Abstract: The fact that there are unicoherent continua which separate $ {E^2}$ is well known, e.g., a circle with a spiral converging onto it is such a continuum. In this paper we extend this pathology by describing a Peano continuum which separates $ {E^3}$ and has the property that however it is written as the union of two unicoherent Peano continua, their intersection is unicoherent.

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Keywords: Unicoherence, 2-coherence, local unicoherence, Čech homology and cohomology
Article copyright: © Copyright 1971 American Mathematical Society

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