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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A topological characterization of the dilation in $E^{n}$


Author: L. S. Husch
Journal: Proc. Amer. Math. Soc. 28 (1971), 234-236
MSC: Primary 57.47
DOI: https://doi.org/10.1090/S0002-9939-1971-0283821-X
MathSciNet review: 0283821
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Abstract: A topological characterization is given to determine whether a homeomorphism of Euclidean $n$-space, $n \ne 4,5$, is topologically equivalent to the dilation $x \to \frac {1}{2}x$.


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Keywords: Dilation, homeomorphisms of <IMG WIDTH="33" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="${E^n}$">, regular homeomorphisms, equicontinuous powers, action of integers on <IMG WIDTH="33" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="${E^n}$">
Article copyright: © Copyright 1971 American Mathematical Society