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 
@article{10_4064_fm_157_1_43_60,
     author = {Jan J. Dijkstra and Kenneth  Kunen and Jan van Mill},
     title = {Hausdorff measures and two point set extensions},
     journal = {Fundamenta Mathematicae},
     pages = {43--60},
     publisher = {mathdoc},
     volume = {157},
     number = {1},
     year = {1998},
     doi = {10.4064/fm-157-1-43-60},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/fm-157-1-43-60/}
}
TY  - JOUR
AU  - Jan J. Dijkstra
AU  - Kenneth  Kunen
AU  - Jan van Mill
TI  - Hausdorff measures and two point set extensions
JO  - Fundamenta Mathematicae
PY  - 1998
SP  - 43
EP  - 60
VL  - 157
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/fm-157-1-43-60/
DO  - 10.4064/fm-157-1-43-60
LA  - en
ID  - 10_4064_fm_157_1_43_60
ER  - 
%0 Journal Article
%A Jan J. Dijkstra
%A Kenneth  Kunen
%A Jan van Mill
%T Hausdorff measures and two point set extensions
%J Fundamenta Mathematicae
%D 1998
%P 43-60
%V 157
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/fm-157-1-43-60/
%R 10.4064/fm-157-1-43-60
%G en
%F 10_4064_fm_157_1_43_60
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. http://geodesic.mathdoc.fr/articles/10.4064/fm-157-1-43-60/

Cité par Sources :