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A Note On Arc-Preserving Functions For Manifolds1

Published online by Cambridge University Press:  20 November 2018

H. J. Charlton
H. J. Charlton*
Affiliation:
North Carolina State University
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Hall and Puckett [2] have shown that an arc - preserving function defined ona locally connected continuum having no local separating points is ahomeomorphism if its total image is not an arc or point. This note showsthat their results can be extended to non-compact manifolds.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 4 , October 1967 , pp. 597 - 598
Copyright
Copyright © Canadian Mathematical Society 1967

Footnotes

1

This result is from the author′s doctoral dissertation, VirginiaPolytechnic Institute, 1966, directed by Professor P. H. Doyle.

References

1. Doyle, P. H. and J. G. Hocking, , A decomposition the or em for n-dimensional manifolds. Proc. Amer. Math. Soc. 13 (1966), 469-471.Google Scholar
2. Hall, D. W. and Puckett, W. T. Jr., Conditions for continuity of arc preserving transformations. Bull. Amer. Math. Soc. 47 (1944), 468-475.Google Scholar