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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Mappings onto the plane


Author: Dix H. Pettey
Journal: Trans. Amer. Math. Soc. 157 (1971), 297-309
MSC: Primary 54.75
Erratum: Trans. Amer. Math. Soc. 162 (1971), 473.
MathSciNet review: 0275395
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Abstract: In this paper, we show that if $ X$ is a connected, locally connected, locally compact topological space and $ f$ is a 1-1 mapping of $ X$ onto $ {E^2}$, then $ f$ is a homeomorphism. Using this result, we obtain theorems concerning the compactness of certain mappings onto $ {E^2}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0275395-9
PII: S 0002-9947(1971)0275395-9
Keywords: One-to-one mapping, monotone mapping, compact mapping, locally connected generalized continuum, inverse system, upper-semicontinuous decomposition, reflexive compact mapping
Article copyright: © Copyright 1971 American Mathematical Society