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

R. Ayala; M. Chávez; A. Quintero

Colloquium Mathematicae (1998)

  • Volume: 75, Issue: 2, page 175-181
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Ayala, R., Chávez, M., and Quintero, A.. "On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor." Colloquium Mathematicae 75.2 (1998): 175-181. <http://eudml.org/doc/210536>.

@article{Ayala1998,
abstract = {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.},
author = {Ayala, R., Chávez, M., Quintero, A.},
journal = {Colloquium Mathematicae},
keywords = {planar; Peano continuum; JFM 56.1141.03; Kuratowski graph},
language = {eng},
number = {2},
pages = {175-181},
title = {On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor},
url = {http://eudml.org/doc/210536},
volume = {75},
year = {1998},
}

TY - JOUR
AU - Ayala, R.
AU - Chávez, M.
AU - Quintero, A.
TI - On the planarity of Peano generalized continua: An extension of a theorem of S. Claytor
JO - Colloquium Mathematicae
PY - 1998
VL - 75
IS - 2
SP - 175
EP - 181
AB - 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.
LA - eng
KW - planar; Peano continuum; JFM 56.1141.03; Kuratowski graph
UR - http://eudml.org/doc/210536
ER -

References

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  1. [1] R. Ayala, A. Márquez and A. Quintero, On the planarity of infinite 2 -complexes, Abh. Math. Sem. Hamburg 67 (1997), 137-148. Zbl0901.52015
  2. [2] S. Claytor, Peanian continua not imbeddable in a spherical surface, Ann. of Math. 38 (1937), 631-646. Zbl0017.19002
  3. [3] G. Dirac and S. Schuster, A theorem of Kuratowski, Indag. Math. 16 (1954), 343-348. 
  4. [4] R. Engelking, General Topology, Heldermann, 1989. 
  5. [5] H. Freudenthal, Über die topologischer Raüme und Gruppen, Math. Z. 33 (1931), 692-713. Zbl57.0731.01
  6. [6] R. Halin, Zur häufungspunktfreien Darstellung abzählbarer Graphen in der Ebene, Arch. Math. (Basel) 17 (1966), 239-243. Zbl0141.40904
  7. [7] K. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271-283. Zbl56.1141.03
  8. [8] S. Mardešić and J. Segal, A note on polyhedra embeddable in the plane, Duke Math. J. 33 (1966), 633-638. Zbl0168.21602
  9. [9] A. W. Schurle, Topics in Topology, North-Holland, 1979. Zbl0443.54001
  10. [10] C. Thomassen, Straightline representations of infinite planar graphs, J. London Math. Soc. 16 (1977), 411-423. Zbl0373.05032

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