### Quotients of valuated vector spaces

Paul Hill
<span title="1981-01-01">1981</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a64sw4kcsveajhudnssdwrwvze" style="color: black;">Proceedings of the American Mathematical Society</a> </i> &nbsp;
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 <•>. 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.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1090/s0002-9939-1981-0589128-1">doi:10.1090/s0002-9939-1981-0589128-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zvn3ept7zjgqljtruupwfcahwi">fatcat:zvn3ept7zjgqljtruupwfcahwi</a> </span>
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