Document Type

Conference Proceeding

Language

eng

Publication Date

8-1983

Publisher

American Mathematical Society

Source Publication

Proceedings of the American Mathematical Society

Source ISSN

0002-9939

Original Item ID

DOI: 10.1090/S0002-9939-1983-0702301-6

Abstract

We investigate the conjecture that the complement in the euclidean plane E2 of a set F of cardinality less than the continuum c can be partitioned into simple closed curves if F has a single point. The case in which F is finite was settled in [1] where it was used to prove that, among the compact connected two-manifolds, only the torus and the Klein bottle can be so partitioned. Here we prove the conjecture in the case where F either has finitely many isolated points or finitely many cluster points. Also we show there exists a self-dense totally disconnected set F of cardinality c and a partition of E2\F into "rectangular" simple closed curves.

Comments

Published version. Proceedings of the American Mathematical Society, Vol. 88, No. 4 (August 1983): 691-697. DOI. © 1983 American Mathematical Society. Used with permission.

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