Abstract
In this chapter we consider relationships between the existence of families of open subsets of a space X and the cellularity of X* =βX\X. Recall that the cellularity of a space Y is the smallest cardinal number m for which each pairwise disjoint family of non-empty open sets of Y has m or fewer members. The density of a space Y is the smallest cardinal number which can be the cardinal number of some dense subspace of Y. It is clear that the density of a space is at least as great as the cellularity. Most of the results will take the form of providing a lower bound for the cellularity of X* by demonstrating the existence of families of pairwise disjoint open sets in X*. The methods used will be reminiscent of that used in Chapter 3 to show that the cellularity of ℕ* is c. In the last sections of the chapter, we will show that there exists a point in ℕ* which belongs to the closure of each member of a family of c pairwise disjoint open sets of ℕ*.
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© 1974 Springer-Verlag Berlin Heidelberg New York
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Walker, R.C. (1974). Cellularity of Growths. In: Walker, R.C. (eds) The Stone-Čech Compactification. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61935-9_5
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DOI: https://doi.org/10.1007/978-3-642-61935-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-61937-3
Online ISBN: 978-3-642-61935-9
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