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

R. Ayala; M. Chávez; A. Quintero — 1998

Colloquium Mathematicae

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.

On the connectivity of skeletons of pseudomanifolds with boundary

R. Ayala; M. J. Chávez; Alberto Márquez; Antonio Quintero — 2002

Mathematica Bohemica

In this note we show that $1$ -skeletons and $2$ -skeletons of $n$ -pseudomanifolds with full boundary are $(n + 1)$ -connected graphs and $n$ -connected $2$ -complexes, respectively. This generalizes previous results due to Barnette and Woon.

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