? 2022 Elsevier B.V.We provide necessary and/or sufficient conditions on vector spaces V of real sequences to be a Fréchet space such that each coordinate map is continuous, that is, to be a locally convex FK space. In particular, we show that if c00(I)?V??∞(I) for some ideal I on ω, then V is a locally convex FK space if and only if there exists an infinite set S?ω for which every infinite subset does not belong to I.
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