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On the Connectedness of the Sets of Limit Points of Certain Transforms of Bounded Sequences(1)

Published online by Cambridge University Press:  20 November 2018

Dany Leviatan  and
Lee Lorch
Dany Leviatan
Affiliation:
University of Illinois, Urbana, Illinois
Lee Lorch
Affiliation:
York University, Toronto, Ontario
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The transforms discussed here are the quasi-Hausdorff (Theorem 1), the [J, ƒ(x)] (Theorem 2) and the Borel integral means (Theorem 3). We are concerned here with whether or not the limit-points of these transforms of bounded sequences form connected sets. Such a set is one which cannot be decomposed into the union of two disjoint nonempty open sets.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 175 - 181
Copyright
Copyright © Canadian Mathematical Society 1971

Footnotes

(1)

This work was assisted by a grant from the National Research Council of Canada.

References

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