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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

``Image of a Hausdorff arc'' is cyclically extensible and reducible


Author: J. L. Cornette
Journal: Trans. Amer. Math. Soc. 199 (1974), 253-267
MSC: Primary 54F30
DOI: https://doi.org/10.1090/S0002-9947-1974-0375257-5
MathSciNet review: 0375257
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Abstract: It is shown that a Hausdorff continuum $ S$ is the continuous image of an arc (respectively arcwise connected) if and only if each cyclic element of $ S$ is the continuous image of an arc (respectively, arcwise connected). Also, there is given an analogue to the metric space cyclic chain approximation theorem of G. T. Whyburn which applies to locally connected Hausdorff continua.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0375257-5
Keywords: Cyclic elements, arcwise connected
Article copyright: © Copyright 1974 American Mathematical Society