### Abstract

If X is a topological space with density d(X)≥2, then cf (d((X^{κ})_{(λ)}))≥cf λ, where (X^{κ})_{(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 language | English |
---|---|

Pages (from-to) | 307-312 |

Number of pages | 6 |

Journal | General Topology and its Applications |

Volume | 9 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1978 |

### Fingerprint

### Keywords

- box product
- density
- family of large oscillation

### Cite this

*General Topology and its Applications*,

*9*(3), 307-312. https://doi.org/10.1016/0016-660X(78)90034-X

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

Research output: Contribution to journal › Article

*General Topology and its Applications*, vol. 9, no. 3, pp. 307-312. https://doi.org/10.1016/0016-660X(78)90034-X

}

TY - JOUR

T1 - On the density of λ-box products

AU - Cater, F. S.

AU - Erdős, P.

AU - Galvin, Fred

PY - 1978

Y1 - 1978

N2 - 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.

AB - 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.

KW - box product

KW - density

KW - family of large oscillation

UR - http://www.scopus.com/inward/record.url?scp=0000483533&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000483533&partnerID=8YFLogxK

U2 - 10.1016/0016-660X(78)90034-X

DO - 10.1016/0016-660X(78)90034-X

M3 - Article

AN - SCOPUS:0000483533

VL - 9

SP - 307

EP - 312

JO - Topology and its Applications

JF - Topology and its Applications

SN - 0166-8641

IS - 3

ER -