Quotients of valuated vector spaces
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- by Paul Hill PDF
- Proc. Amer. Math. Soc. 81 (1981), 14-18 Request permission
Abstract:
This paper has three purposes. The first is to present a direct example of a quotient of an injective space that is not itself injective. The second is to demonstrate that Theorem 3 in [2] is false. An $s$-dense subspace $S$ of a free space $F$ is not free by virtue of $F/S$ having only values that are cofinal with $\omega$. Finally, we furnish a valid proof, independent of the aforementioned Theorem 3, that a subspace $V$ of a free space is free if $V$ satisfies Fuchs’ countability condition.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 14-18
- MSC: Primary 18G05; Secondary 15A03, 18G20, 20K10
- DOI: https://doi.org/10.1090/S0002-9939-1981-0589128-1
- MathSciNet review: 589128