The relationships of spans of convex continua in $\textbf {R}^ n$
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- by Thelma West PDF
- Proc. Amer. Math. Soc. 111 (1991), 261-265 Request permission
Abstract:
It has been conjectured that ${\sigma ^ * }(X) \geq \tfrac {1}{2}\sigma _0^ * (X)$ for each nonempty connected metric space $X$. In this paper we show that ${\sigma ^ * }(X) \geq \tfrac {{\sqrt {13} }}{4}\sigma _0^ * (X)$ for each convex continuum $X$ in ${R^n}$. We also show that under certain conditions a lower bound for the ratio ${\sigma ^ * }(X)/\sigma _0^ * (X)$ is larger than $\tfrac {{\sqrt {13} }}{4}$. It has also been conjectured that ${\sigma ^ * }(X) \geq \sigma (X)/2$ and that $\sigma _0^ * (X) \geq {\sigma _0}(X)/2$ for each nonempty connected metric space $X$. We show that these two inequalities hold when $X$ is a convex continuum in ${R^n}$.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 261-265
- MSC: Primary 54F15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1037227-9
- MathSciNet review: 1037227