## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  394.54002
Autor:  Cater, F.S.; Erdös, Paul; Galvin, Fred
Title:  On the density of \lambda-box products. (In English)
Source:  General Topol. Appl. 9, 307-312 (1978).
Review:  If X is a topological space with density d(X) \geq 2, then cf(d((X\kappa)(\lambda))) \geq cf\lambda, where (X\kappa)(\lambda) is the \lambda-box product of \kappa copies of X. We use this observation to get lower bounds for the function \delta(\kappa,\lambda) = d((D(2)\kappa)(\lambda)), where D(2) is the discrete space {0,1}. It turns out that \delta(\kappa,\lambda) is usually (if not always) equal to the well-known upper bound (log\kappa) < \lambda. We also answer a question of W.W.Comfort and S.Negrepontis [The theory of ultrafilters (1974; Zbl 298.02004) Sect. 3, p. 79] about necessary and sufficient conditions for \delta(\kappa^+,\lambda) \leq \kappa.
Classif.:  * 54A25 Cardinality properties of topological spaces
54B10 Product spaces (general topology)
Keywords:  density of lambda-box products
Citations:  Zbl.298.02004

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