On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor
Ayala, R. ; Chávez, M. ; Quintero, A.
Colloquium Mathematicae, Tome 78 (1998), p. 175-181 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

We extend a theorem of S. Claytor in order to characterize the Peano generalized continua which are embeddable into the 2-sphere. We also give a characterization of the Peano generalized continua which admit closed embeddings in the Euclidean plane.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:210536 
@article{bwmeta1.element.bwnjournal-article-cmv75z2p175bwm,
     author = {R. Ayala and M. Ch\'avez and A. Quintero},
     title = {On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor},
     journal = {Colloquium Mathematicae},
     volume = {78},
     year = {1998},
     pages = {175-181},
     zbl = {0923.54028},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv75z2p175bwm}
}

Ayala, R.; Chávez, M.; Quintero, A. On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor. Colloquium Mathematicae, Tome 78 (1998) pp. 175-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv75z2p175bwm/

[000] [1] R. Ayala, A. Márquez and A. Quintero, On the planarity of infinite 2-complexes, Abh. Math. Sem. Hamburg 67 (1997), 137-148. | Zbl 0901.52015

[001] [2] S. Claytor, Peanian continua not imbeddable in a spherical surface, Ann. of Math. 38 (1937), 631-646. | Zbl 0017.19002

[002] [3] G. Dirac and S. Schuster, A theorem of Kuratowski, Indag. Math. 16 (1954), 343-348.

[003] [4] R. Engelking, General Topology, Heldermann, 1989.

[004] [5] H. Freudenthal, Über die topologischer Raüme und Gruppen, Math. Z. 33 (1931), 692-713. | Zbl 57.0731.01

[005] [6] R. Halin, Zur häufungspunktfreien Darstellung abzählbarer Graphen in der Ebene, Arch. Math. (Basel) 17 (1966), 239-243. | Zbl 0141.40904

[006] [7] K. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271-283. | Zbl 56.1141.03

[007] [8] S. Mardešić and J. Segal, A note on polyhedra embeddable in the plane, Duke Math. J. 33 (1966), 633-638. | Zbl 0168.21602

[008] [9] A. W. Schurle, Topics in Topology, North-Holland, 1979. | Zbl 0443.54001

[009] [10] C. Thomassen, Straightline representations of infinite planar graphs, J. London Math. Soc. 16 (1977), 411-423. | Zbl 0373.05032