On partitions of plane sets into simple closed curves. II

Author:
Paul Bankston

Journal:
Proc. Amer. Math. Soc. **89** (1983), 498-502

MSC:
Primary 54B15; Secondary 57N05

Addendum:
Proc. Amer. Math. Soc. **91** (1984), 658.

MathSciNet review:
715874

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Abstract: We answer some questions raised in [**1**]. In particular, we prove: (i) Let be a compact subset of the euclidean plane such that no component of separates . Then can be partitioned into simple closed curves iff is nonempty and connected. (ii) Let be any subset which is not dense in , and let be a partition of into simple closed curves. Then has the cardinality of the continuum. We also discuss an application of (i) above to the existence of flows in the plane.

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0715874-4

Keywords:
Topological partitions,
euclidean plane,
simple closed curves,
continuous flows

Article copyright:
© Copyright 1983
American Mathematical Society