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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 1-dimensional Peano continuum which is not an IFS attractor


Authors: Taras Banakh and Magdalena Nowak
Journal: Proc. Amer. Math. Soc. 141 (2013), 931-935
MSC (2010): Primary 28A80, 54D05, 54F50, 54F45
Published electronically: July 16, 2012
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Abstract: Answering an old question of M. Hata, we construct an example of a 1-dimensional Peano continuum which is not homeomorphic to an attractor of IFS.


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Additional Information

Taras Banakh
Affiliation: Instytut Matematyki, Jan Kochanowski University, Kielce, Poland – and – Ivan Franko National University of Lviv, Ukraine
Email: t.o.banakh@gmail.com

Magdalena Nowak
Affiliation: Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Łojasiewicza 6, 30-348 Kraków, Poland, – and – Jan Kochanowski University, ul. Świętokrzyska 15, 25-406 Kielce, Poland
Email: magdalena.nowak805@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11737-X
PII: S 0002-9939(2012)11737-X
Keywords: Fractal, Peano continuum, Iterated Function System, IFS-attractor
Received by editor(s): July 19, 2011
Published electronically: July 16, 2012
Additional Notes: The first author has been partially financed by NCN means, granted by decision DEC-2011/01/B/ST1/01439
The second author was supported by the ESF Human Capital Operational Programme grant 6/1/8.2.1./POKL/2009
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.