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One-dimensional nonseparating plane continua with disjoint ε-dense subcontinua

Topology and its Applications (1991) 39(2) 145-151
DOI: 10.1016/0166-8641(91)90014-D
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Abstract

The following theorem is proved: suppose X is a one-dimensional nonseparating plane continuum such that for any ε > 0, X has two disjoint ε-dense subcontinua. Then X is either indecomposable or the union of two indecomposable continua. The result is used to address a question of Knaster. © 1991.

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Curry, S. B. (1991). One-dimensional nonseparating plane continua with disjoint ε-dense subcontinua. Topology and Its Applications, 39(2), 145–151. https://doi.org/10.1016/0166-8641(91)90014-D

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