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Finite and \(\omega\)-resolvability. (English) Zbl 0856.54010

Modifying terminology of E. Hewitt [Duke Math. J. 10, 309-333 (1943; Zbl 0060.39407), one says for a cardinal \(\kappa\) that a space \(X\) is \(\kappa\)-resolvable if \(X\) admits a family of \(\kappa\)-many pairwise disjoint dense subsets. In this useful, much-cited paper, the author shows that every space which is \(k\)-resolvable for each \(k<\omega\) is \(\omega\)-resolvable.

MSC:

54B05 Subspaces in general topology
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)

Citations:

Zbl 0060.39407
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References:

[1] J. Ceder and T. Pearson, On products of maximally resolvable spaces, Pacific J. Math. 22 (1967), 31 – 45. · Zbl 0153.24201
[2] W. W. Comfort and Li Feng, The union of resolvable spaces is resolvable, Math. Japon. 38 (1993), no. 3, 413 – 414. · Zbl 0769.54002
[3] A. G. El\(^{\prime}\)kin, Resolvable spaces which are not maximally resolvable, Vestnik Moskov. Univ. Ser. I Mat. Meh. 24 (1969), no. 4, 66 – 70 (Russian, with English summary). · Zbl 0183.51204
[4] E. Hewitt, A problem in set-theoretic topology, Duke Math. J. 10 (1943), 309–333. · Zbl 0060.39407
[5] Eric K. van Douwen, Applications of maximal topologies, Topology Appl. 51 (1993), no. 2, 125 – 139. · Zbl 0845.54028
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