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.References
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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