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A Remark on the Existence of a Denumerable Base for a Family of Functions

Published online by Cambridge University Press:  20 November 2018

Fritz Rothberger
Fritz Rothberger*
Affiliation:
University of New Brunswick
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Extract

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A family F of functions is said to have a denumerable base if there exists a sequence of functions {fn(x)} (not necessarily ∈ F) such that any function f ∈ F is the limit of a subsequence of {fn (x)}. The domain X of a function f(x) is the set of x´s for which f(x) is defined ; we say f(x) is a function on X. A dyadic function is a function taking only the values 0 and 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 4 , 1952 , pp. 117 - 119
Copyright
Copyright © Canadian Mathematical Society 1952

References

1. Rothberger, F., On families of real functions with a denumerable base, Ann. Math., vol. 45 (1944), 397–406.Google Scholar