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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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Extract

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Hall and Puckett [2] have shown that an arc - preserving function defined on a locally connected continuum having no local separating points is a homeomorphism if its total image is not an arc or point. This note shows that their results can be extended to non-compact manifolds.

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, Virginia Polytechnic 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