On the density of λ-box products

F. S. Cater, P. Erdős, Fred Galvin

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

If X is a topological space with density d(X)≥2, then cf (d((Xκ)(λ)))≥cf λ, where (Xκ)(λ) is the λ-box product of κ copies of X. We use this observation to get lower bounds for the function δ(κ, λ)=d((D(2)κ)(λ)), where D(2) is the discrete space {0, 1}. It turns out that δ(κ, λ) is usually (if not always) equal to the well-known upper bound (log κ). We also answer a question of Confort and Negrepontis about necessary and sufficient conditions for δ(κ+, λ)≤κ.

Original languageEnglish
Pages (from-to)307-312
Number of pages6
JournalGeneral Topology and its Applications
Volume9
Issue number3
DOIs
Publication statusPublished - 1978

Fingerprint

Box Product
Topological space
Lower bound
Upper bound
Necessary Conditions
Sufficient Conditions
Observation

Keywords

  • box product
  • density
  • family of large oscillation

Cite this

On the density of λ-box products. / Cater, F. S.; Erdős, P.; Galvin, Fred.

In: General Topology and its Applications, Vol. 9, No. 3, 1978, p. 307-312.

Research output: Contribution to journalArticle

Cater, F. S. ; Erdős, P. ; Galvin, Fred. / On the density of λ-box products. In: General Topology and its Applications. 1978 ; Vol. 9, No. 3. pp. 307-312.
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