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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the dimensions of projections of compact subsets of $\textbf {R}^{m}$
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by Y. Sternfeld PDF
Proc. Amer. Math. Soc. 88 (1983), 735-742 Request permission

Abstract:

In this note we continue the study of a problem considered earlier by G. Nöbling, S. Mardešić, C. Pixley and the author. Let $W$ be an $n$-dimensional compact subset of ${{\mathbf {R}}^m}$, and let $\{ {i_1},{i_2}, \ldots ,{i_k}\} \subset \{ 1,2, \ldots ,m\}$. It is shown that if the projection ${P_{i1,i2, \ldots ,ik}}$ satisfies a certain condition called normality on $W$, then there exist ${i_{k + 1}}$, ${i_{k + 2}}, \ldots ,{i_n}$ so that $\dim {P_{i1,i2, \ldots ,{i_k},{i_{k + 1}}, \ldots ,{i_n}}}(W) = n$. It is also shown that at least $(_k^n)$ such normal projections do exist (for $1 \leqslant k \leqslant n$), and an example is constructed to show that the normality condition is not necessary.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 88 (1983), 735-742
  • MSC: Primary 54F45
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0702310-7
  • MathSciNet review: 702310