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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A characterization of the $ 2$-sphere in terms of Jordan curve separation


Author: Carsten Thomassen
Journal: Proc. Amer. Math. Soc. 115 (1992), 863-864
MSC: Primary 57N05; Secondary 54F65
MathSciNet review: 1124153
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Abstract: We show that, up to homeomorphism, the $ 2$-sphere is the only compact arcwise connected metric space $ X$ satisfying (i) If $ J$ is a simple arc in $ X$, then $ X\backslash J$ is arcwise connected;

(ii) If $ J$ is a simple closed curve in $ X$, then $ X\backslash J$ is disconnected (in the sense that $ X\backslash J$ contains a proper nonempty subset that is both open and closed).


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1124153-0
PII: S 0002-9939(1992)1124153-0
Article copyright: © Copyright 1992 American Mathematical Society