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Incomplete reflexive spaces without Schauder bases

Published online by Cambridge University Press:  24 October 2008

R. J. Knowles  and
T. A. Cook
R. J. Knowles
Affiliation:
University of Connecticut, Waterbury Branch, Waterbury, Connecticut
T. A. Cook
Affiliation:
University of Massachusetts, Department of Mathematics, Amherst, Massachusetts
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Extract

In 1968, Amemiya and Kōmura ((1), p. 275) gave an example of a separable and incomplete Montel space. Their example depended upon constructing a subspace of ω, the countable product of real lines, which had several properties and in particular had codimension in ω. There is an error on page 276, line 5 of the proof of the Hilfssatz concerning this construction. The constructed subspace has codimension one. A more delicate construction is needed here; in fact, an example given by Webb ((7), p. 360) is sufficient to make this correction.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 83 - 86
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

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