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Portugaliae Mathematica

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Volume 65, Issue 2, 2008, pp. 237–242
DOI: 10.4171/PM/1808

Published online: 2008-06-30

Steiner's invariants and minimal connections

Stephen Ducret[1] and Marc Troyanov[2]

(1) Ecole Polytechnique Fédérale de Lausanne, Switzerland
(2) Ecole Polytechnique Fédérale de Lausanne, Switzerland

The aim of this note is to prove that any compact metric space can be made connected at a minimal cost, where the cost is taken to be the one-dimensional Hausdorff measure.

Keywords: Metric geometry, Steiner invariant

Ducret Stephen, Troyanov Marc: Steiner's invariants and minimal connections. Port. Math. 65 (2008), 237-242. doi: 10.4171/PM/1808