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Proceedings of the American Mathematical Society

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

 

 

Transcendental extensions of field topologies on countable fields


Author: Klaus-Peter Podewski
Journal: Proc. Amer. Math. Soc. 39 (1973), 39-41
MSC: Primary 12J99
DOI: https://doi.org/10.1090/S0002-9939-1973-0311634-0
MathSciNet review: 0311634
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Abstract: Let $ \mathcal{T}$ be a field topology on a countable field $ K$ and let $ K(x)$ be a simple transcendental extension of $ K$. Then there exists a field topology $ \mathcal{T}'$ for $ K(x)$ such that $ \mathcal{T}' \upharpoonleft K = \mathcal{T}$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0311634-0
Article copyright: © Copyright 1973 American Mathematical Society