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Proceedings of the American Mathematical Society

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

 

 

The domain rank of open surfaces of infinite genus


Author: Richard J. Tondra
Journal: Proc. Amer. Math. Soc. 28 (1971), 581-583
MSC: Primary 57A05
DOI: https://doi.org/10.1090/S0002-9939-1971-0296920-3
MathSciNet review: 0296920
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Abstract: In a recent paper it was shown that an open surface, i.e. a connected $ 2$-manifold without boundary, has finite domain rank if and only if it has finite genus. In the present paper, it is shown that the domain rank of any open surface of infinite genus is countably infinite.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0296920-3
Keywords: Domain, domain rank, surface, ideal boundary
Article copyright: © Copyright 1971 American Mathematical Society