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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

$ F$-spaces universal with respect to linear codimension


Author: Wesley E. Terry
Journal: Proc. Amer. Math. Soc. 63 (1977), 59-65
MSC: Primary 46A15
DOI: https://doi.org/10.1090/S0002-9939-1977-0442627-4
MathSciNet review: 0442627
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1977-0442627-4
Article copyright: © Copyright 1977 American Mathematical Society