On Partitions of Plane Sets into Simple Closed Curves II

Authors

Paul Bankston, Marquette UniversityFollow

Document Type

Conference Proceeding

Language

eng

Publication Date

11-1983

Publisher

American Mathematical Society

Source Publication

Proceedings of the American Mathematical Society

Source ISSN

0002-9939

Original Item ID

10.2307/2274179

Abstract

We answer some questions raised in [1]. In particular, we prove: (i) Let F be a compact subset of the euclidean plane E² such that no component of F separates E². Then E²\F can be partitioned into simple closed curves iff F is nonempty and connected. (ii) Let F Ç E² be any subset which is not dense in E², and let S be a partition of E²\F into simple closed curves. Then S has the cardinality of the continuum. We also discuss an application of (i) above to the existence of flows in the plane.

Comments

Published version. Proceedings of the American Mathematical Society, Vol. 89, No. 3 (November 1983): 498-502. DOI. © 1983 American Mathematical Society. Used with permission.

Recommended Citation

Bankston, Paul, "On Partitions of Plane Sets into Simple Closed Curves II" (1983). Mathematics, Statistics and Computer Science Faculty Research and Publications. 130.
https://epublications.marquette.edu/mscs_fac/130