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

 

Plane continua and totally disconnected sets of buried points


Authors: Jan van Mill and Murat Tuncali
Journal: Proc. Amer. Math. Soc. 140 (2012), 351-356
MSC (2010): Primary 54F15, 54H20, 37B45
Published electronically: May 12, 2011
MathSciNet review: 2833545
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Abstract: It is shown that there is a continuum in the plane whose set of buried points is totally disconnected and weakly 1-dimensional, but not zero-dimensional. This answers a problem of Curry, Mayer and Tymchatyn.


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Additional Information

Jan van Mill
Affiliation: Department of Mathematics, Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
Email: vanmill@few.vu.nl

Murat Tuncali
Affiliation: Department of Computer Science and Mathematics, Nipissing University, 100 College Drive, North Bay, ON, P1B 8L7, Canada
Email: muratt@nipissingu.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11041-4
PII: S 0002-9939(2011)11041-4
Keywords: Buried point, totally disconnected, plane continuum, zero-dimensional, Kuratowski’s set
Received by editor(s): November 5, 2010
Published electronically: May 12, 2011
Additional Notes: The first author is pleased to thank the Department of Mathematics and Computer Science at Nipissing University for generous hospitality and support.
The second author is partially supported by National Science and Engineering Research Council of Canada grant No. 141066-2000
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.