On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor

• Autorzy: R. Ayala , M. J. Chávez , A. Quintero
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1998
• Tom: 75
• Numer: 2
• Strony: 175-181

Daty

wydano

1998

poprawiono

1996-05-06

poprawiono

1997-04-15

Twórcy

autor

R. Ayala

• Departamento de Matemática Aplicada I, Escuela Universitaria de Arquitectura Técnica, Universidad de Sevilla Avda., Reina Mercedes s/n, 41012-Sevilla Spain

autor

M. J. Chávez

• Departamento de Matemática Aplicada I, Escuela Universitaria de Arquitectura Técnica, Universidad de Sevilla Avda., Reina Mercedes s/n, 41012-Sevilla Spain

autor

A. Quintero

• Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Apartado 1160, 41080-Sevilla, Spain

Bibliografia

• [1] R. Ayala, A. Márquez and A. Quintero, On the planarity of infinite $2$-complexes, Abh. Math. Sem. Hamburg 67 (1997), 137-148.
• [2] S. Claytor, Peanian continua not imbeddable in a spherical surface, Ann. of Math. 38 (1937), 631-646.
• [3] G. Dirac and S. Schuster, A theorem of Kuratowski, Indag. Math. 16 (1954), 343-348.
• [4] R. Engelking, General Topology, Heldermann, 1989.
• [5] H. Freudenthal, Über die topologischer Raüme und Gruppen, Math. Z. 33 (1931), 692-713.
• [6] R. Halin, Zur häufungspunktfreien Darstellung abzählbarer Graphen in der Ebene, Arch. Math. (Basel) 17 (1966), 239-243.
• [7] K. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271-283.
• [8] S. Mardešić and J. Segal, A note on polyhedra embeddable in the plane, Duke Math. J. 33 (1966), 633-638.
• [9] A. W. Schurle, Topics in Topology, North-Holland, 1979.
• [10] C. Thomassen, Straightline representations of infinite planar graphs, J. London Math. Soc. 16 (1977), 411-423.