Document Type

Conference Proceeding

Language

eng

Format of Original

5 p.

Publication Date

11-1983

Publisher

American Mathematical Society

Source Publication

Proceedings of the American Mathematical Society

Source ISSN

0002-9939

Original Item ID

doi: 10.1090/S0002-9939-1983-0715874-4; Shelves: QA1 .A5215 Storage S

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. © American Mathematical Society 1983. Used with permission.

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