24 Citations
Average distances in compact connected spaces
- MathematicsBulletin of the Australian Mathematical Society
- 1982
We give a simple proof of the fact that compact, connected topological spaces have the “average distance property”. For a metric space (X, d), this asserts the existence of a unique number a = a(X)…
Rendezvous Numbers of Metric Spaces – a Potential Theoretic Approach
- Mathematics
- 2005
The present work draws on the understanding how notions of general potential theory – as set up, e.g., by Fuglede – explain existence and some basic results on the " magical " rendezvous numbers. We…
Rendezvous numbers of metric spaces – a potential theoretic approach
- Mathematics
- 2005
Abstract.The present work draws on the understanding how notions of general potential theory – as set up, e.g., by Fuglede – explain existence and some basic results on the “magical” rendezvous…
The average distance property of the spaces
$ \ell _\infty ^n ({\Bbb C}) $ and
$ \ell _1^n ({\Bbb C}) $
- Mathematics
- 2001
Abstract. In this note we calculate the exact values of the rendezvous numbers of the Banach spaces
$ \ell _\infty ^n({\Bbb C}) $ and
$ \left({1\over 3}+{{2\sqrt 3}\over{\pi }}\right) $, and
$…
NUMERICAL GEOMETRY-NUMBERS FOR SHAPES
- Mathematics
- 1986
(1986). Numerical Geometry-Numbers for Shapes. The American Mathematical Monthly: Vol. 93, No. 4, pp. 260-275.
Distance geometry in quasihypermetric spaces. III
- Mathematics
- 2011
Let (X, d) be a compact metric space and let \documentclass{article}\usepackage{amssymb}\pagestyle{empty}\begin{document}$\mathcal {M}(X)$\end{document} denote the space of all finite signed Borel…
DISTANCE GEOMETRY IN QUASIHYPERMETRIC SPACES. I
- Mathematics
- 2009
Let ( X , d ) be a compact metric space and let ℳ( X ) denote the space of all finite signed Borel measures on X . Define I :ℳ( X )→ℝ by and set M ( X )=sup I ( μ ), where μ ranges over the…
Distance geometry in quasihypermetric spaces. II
- Mathematics
- 2008
Let (X, d) be a compact metric space and let ${\cal M}(X)$ denote the space of all finite signed Borel measures on X. Define…
Transfinite Diameter, Chebyshev Constant and Energy on Locally Compact Spaces
- Mathematics
- 2007
We study the relationship between transfinite diameter, Chebyshev constant and Wiener energy in the abstract linear potential analytic setting pioneered by Choquet, Fuglede and Ohtsuka. It turns out…