DIMENSIONALLY INVARIANT SPACES

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Published: May 15, 2009
DOI: https://doi.org/10.14403/jcms.2009.22.2.245
Keywords:
coding space, ultra metric space, distribution set, Hausdorff dimension, packing dimension, complete bounded Vitali covering
Mathematics Subject Classification (2020):
Primary 28A78, Secondary 54E50

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In Soo Baek
Department of Mathematics, Pusan University of Foreign Studies

Abstract





We consider a code function from the unit interval which has a generalized dyadic expansion into a coding space which has an associated ultra metric. The code function is not a biLipschitz map but a dimension-preserving map in the sense that the Hausdorff and packing dimensions of any subset in the unit interval and its image under the code function coincide respectively.





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Article Details

Issue
Vol. 22 No. 2 (2009)
Section
Articles