Geodesic
Hausdorff measures and two point set extensions
Fundamenta Mathematicae, Tome 157 (1998) no. 1, pp. 43-60

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We investigate the following question: under which conditions is a σ-compact partial two point set contained in a two point set? We show that no reasonable measure or capacity (when applied to the set itself) can provide a sufficient condition for a compact partial two point set to be extendable to a two point set. On the other hand, we prove that under Martin's Axiom any σ-compact partial two point set such that its square has Hausdorff 1-measure zero is extendable.
DOI : 10.4064/fm-157-1-43-60

Jan J. Dijkstra 1 ; Kenneth Kunen 1 ; Jan van Mill 1

1 
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Jan J. Dijkstra; Kenneth  Kunen; Jan van Mill. Hausdorff measures and two point set extensions. Fundamenta Mathematicae, Tome 157 (1998) no. 1, pp. 43-60. doi: 10.4064/fm-157-1-43-60

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