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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A generalization of the Hahn-Mazurkiewicz theorem


Author: L. E. Ward
Journal: Proc. Amer. Math. Soc. 58 (1976), 369-374
MSC: Primary 54F25
DOI: https://doi.org/10.1090/S0002-9939-1976-0413063-0
MathSciNet review: 0413063
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Abstract: It is proved that if a Hausdorff continuum $ X$ can be approximated by finite trees (see the text for definition) then there exists a (generalized) arc $ L$ and a continuous surjection $ \varphi :L \to X$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0413063-0
Keywords: Hahn-Mazurkiewicz theorem, continuum, arc, continuous image of an arc, approximation by finite trees, approximation by a sequence of finite dendrites, inverse limit
Article copyright: © Copyright 1976 American Mathematical Society