ABSTRACT
This note is written to answer the question raised by C. Aull at the American Mathematical Society meeting in Cincinnati, namely, can every disjoint family of zero sets in ℝ be extended to a disjoint family of zero sets in βℝ ? See [1] for context of question. The answer to this question is “no”; and to show this we will construct a family of zero sets Ζα in ℝ such that any zero-set extension in βℝ of the natural numbers ℕ must intersect the closure in βℝ of some Ζα.
