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

top
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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.