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Embeddings of $ n$-dimensional separable metric spaces into the product of Sierpinski curves

Author: Daria Michalik
Journal: Proc. Amer. Math. Soc. 135 (2007), 2661-2664
MSC (2000): Primary 54F45, 14C55; Secondary 54C25, 54F50
Published electronically: March 30, 2007
MathSciNet review: 2302589
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Abstract: We give a short proof of the following fact: the set of embeddings of any $ n$-dimensional separable metric space $ X$ into a certain $ n$-dimensional subset of the $ (n+1)$-product of Sierpinski curves $ \Sigma $ is residual in $ C(X, \Sigma ^{n+1})$.

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Additional Information

Daria Michalik
Affiliation: Institute of Mathematics, Polish Academy of Sciences, P.O. Box 21 Śniadeckich 8 00-956 Warszawa, Poland

Keywords: Covering dimension, Sierpi\'{n}ski curve, embedding, ANR
Received by editor(s): March 21, 2005
Received by editor(s) in revised form: April 28, 2005
Published electronically: March 30, 2007
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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