Generic Partial Two-Point Sets Are Extendable
Canadian mathematical bulletin, Tome 42 (1999) no. 1, pp. 46-51

Voir la notice de l'article provenant de la source Cambridge University Press

It is shown that under $\text{ZFC}$ almost all planar compacta that meet every line in at most two points are subsets of sets that meet every line in exactly two points. This result was previously obtained by the author jointly with K. Kunen and J. vanMill under the assumption that Martin’s Axiom is valid.
DOI : 10.4153/CMB-1999-005-1
Mots-clés : 57N05
Dijkstra, Jan J. Generic Partial Two-Point Sets Are Extendable. Canadian mathematical bulletin, Tome 42 (1999) no. 1, pp. 46-51. doi: 10.4153/CMB-1999-005-1
@article{10_4153_CMB_1999_005_1,
     author = {Dijkstra, Jan J.},
     title = {Generic {Partial} {Two-Point} {Sets} {Are} {Extendable}},
     journal = {Canadian mathematical bulletin},
     pages = {46--51},
     year = {1999},
     volume = {42},
     number = {1},
     doi = {10.4153/CMB-1999-005-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-005-1/}
}
TY  - JOUR
AU  - Dijkstra, Jan J.
TI  - Generic Partial Two-Point Sets Are Extendable
JO  - Canadian mathematical bulletin
PY  - 1999
SP  - 46
EP  - 51
VL  - 42
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-005-1/
DO  - 10.4153/CMB-1999-005-1
ID  - 10_4153_CMB_1999_005_1
ER  - 
%0 Journal Article
%A Dijkstra, Jan J.
%T Generic Partial Two-Point Sets Are Extendable
%J Canadian mathematical bulletin
%D 1999
%P 46-51
%V 42
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1999-005-1/
%R 10.4153/CMB-1999-005-1
%F 10_4153_CMB_1999_005_1

[1] [1] Dijkstra, J. J., Kunen, K., and van Mill, J., Hausdorff measures and two point set extensions. Fund. Math. 157 (1998), 43–60. Google Scholar

[2] [2] Dijkstra, J. J. and van Mill, J., Two point set extensions—a counterexample. Proc. Amer.Math. Soc. 125 (1997), 2501–2502. Google Scholar

[3] [3] Mazurkiewicz, S., O pewnej mnogósci płaskiej, która ma z każda prosta dwa i tylko dwa punkty wspólne. C. R. Varsovie 7 (1914), 382–384; Polish; French transl. Sur un ensemble plan qui a avec chaque droite deux et seulement deux points communs. Stefan Mazurkiewicz, Traveaux de Topologie et ses Applications, PWN, Warsaw, 1969, 46–47. Google Scholar

Cité par Sources :