Quotients of valuated vector spaces

Hill, Paul

doi:10.1090/S0002-9939-1981-0589128-1

Quotients of valuated vector spaces
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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.

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