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Dense scales of functions

Published online by Cambridge University Press:  09 April 2009

C. A. Rogers
C. A. Rogers
Affiliation:
University College, Gower Street, London W.C.I.
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In a recent paper [1] on scales of functions (which will be called SF for short) P. Erdös C. A. Rogers and S. J. Taylor developed the theory of scales of functions and used the Continuum Hypothesis to establish the existence of scales of functions having certain desirable properties. One of these properties was that of being dense in a certain sense. In the course of some joint work Taylor and I have felt the need for scales which are dense in a rather stronger sense. The object of this note is to indicate how the methods of SF can be used to show that the Continuum Hypothesis implies the existence of scales with the required properties.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 2 , Issue 2 , October 1961 , pp. 137 - 142
Copyright
Copyright © Australian Mathematical Society 1961

References

[1]Erdos, P., Rogers, C. A. and Taylor, S. J., Scales of functions, Australian Journal of Mathematics 1 (1960) 396.Google Scholar