𝐹-spaces universal with respect to linear codimension

Terry, Wesley E.

doi:10.1090/S0002-9939-1977-0442627-4

$F$-spaces universal with respect to linear codimension
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Proc. Amer. Math. Soc. 63 (1977), 59-65 Request permission

Abstract:

Rolewicz raised the question in [5] as to whether there existed a separable F-space ${X_0}$ such that any other separable F-space Y is the image of ${X_0}$ under a continuous linear operator. This can be equivalently phrased as the question [5, Problem II.4.3, p. 47]: Does there exist a separable F-space universal for all separable F-spaces with respect to linear codimension? Theorem 1 proves the existence of such a separable F-space. Theorem 2 generalizes this idea to larger cardinals.

References

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Eine Bemerkung über die Räume vom typus

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