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
HTML articles powered by AMS MathViewer

by Wesley E. Terry

Proc. Amer. Math. Soc. 63 (1977), 59-65

DOI: https://doi.org/10.1090/S0002-9939-1977-0442627-4

PDF | 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

Zur Theorie der linearen Dimension

4

C. Bessaga, On topological classification of complete linear metric spaces, Fund. Math. 56 (1964/65), 251–288. MR 178322, DOI 10.4064/fm-56-3-250-288

Eine Bemerkung über die Räume vom typus

F

7

V. Klee, Mappings into normed linear spaces, Fund. Math. 49 (1960/61), 25–34. MR 126690, DOI 10.4064/fm-49-1-25-34
Stefan Rolewicz, Metric linear spaces, 2nd ed., PWN—Polish Scientific Publishers, Warsaw; D. Reidel Publishing Co., Dordrecht, 1984. MR 802450
Wesley E. Terry, Conditions for a TVS to be homeomorphic with its countable product, Trans. Amer. Math. Soc. 190 (1974), 233–242. MR 338725, DOI 10.1090/S0002-9947-1974-0338725-8