# 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

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topAyala, 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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- [7] K. Kuratowski, Sur le problème des courbes gauches en topologie, Fund. Math. 15 (1930), 271-283. Zbl56.1141.03
- [8] S. Mardešić and J. Segal, A note on polyhedra embeddable in the plane, Duke Math. J. 33 (1966), 633-638. Zbl0168.21602
- [9] A. W. Schurle, Topics in Topology, North-Holland, 1979. Zbl0443.54001
- [10] C. Thomassen, Straightline representations of infinite planar graphs, J. London Math. Soc. 16 (1977), 411-423. Zbl0373.05032

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