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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 circle is not the generalized inverse limit of a subset of $ [0,1]^{2}$


Author: Alejandro Illanes
Journal: Proc. Amer. Math. Soc. 139 (2011), 2987-2993
MSC (2010): Primary 54C60; Secondary 54F15
Published electronically: March 22, 2011
MathSciNet review: 2801638
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Abstract: In this paper we show that the simple closed curve cannot be obtained as the inverse limit of an upper semi-continuous multivalued function from $ [0,1]$ into $ [0,1]$.


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Additional Information

Alejandro Illanes
Affiliation: Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, Ciudad Universitaria, México 04510, D.F.
Email: illanes@matem.unam.mx

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10876-1
PII: S 0002-9939(2011)10876-1
Keywords: Inverse limits, Hilbert cube, simple closed curve, unit square, upper semi-continuous, set valued functions
Received by editor(s): October 8, 2009
Received by editor(s) in revised form: March 26, 2010
Published electronically: March 22, 2011
Additional Notes: The author wishes to thank Gabriela Sanginés for her technical help during the preparation of this paper.
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society