# On character and chain conditions in images of products

Fundamenta Mathematicae (1998)

- Volume: 158, Issue: 1, page 41-49
- ISSN: 0016-2736

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topBell, Murray. "On character and chain conditions in images of products." Fundamenta Mathematicae 158.1 (1998): 41-49. <http://eudml.org/doc/212301>.

@article{Bell1998,

abstract = {A scadic space is a Hausdorff continuous image of a product of compact scattered spaces. We complete a theorem begun by G. Chertanov that will establish that for each scadic space X, χ(X) = w(X). A ξ-adic space is a Hausdorff continuous image of a product of compact ordinal spaces. We introduce an either-or chain condition called Property $R_λ^\{\prime \}$ which we show is satisfied by all ξ-adic spaces. Whereas Property $R_λ^\{\prime \}$ is productive, we show that a weaker (but more natural) Property $R_λ$ is not productive. Polyadic spaces are shown to satisfy a stronger chain condition called Property $R_λ^\{\prime \prime \}$. We use Property $R_λ^\{\prime \}$ to show that not all compact, monolithic, scattered spaces are ξ-adic, thus answering a question of Chertanov’s.},

author = {Bell, Murray},

journal = {Fundamenta Mathematicae},

keywords = {compact; scattered; products; chain condition; ordinals; product of compact scattered spaces; weight; character; dyadic spaces},

language = {eng},

number = {1},

pages = {41-49},

title = {On character and chain conditions in images of products},

url = {http://eudml.org/doc/212301},

volume = {158},

year = {1998},

}

TY - JOUR

AU - Bell, Murray

TI - On character and chain conditions in images of products

JO - Fundamenta Mathematicae

PY - 1998

VL - 158

IS - 1

SP - 41

EP - 49

AB - A scadic space is a Hausdorff continuous image of a product of compact scattered spaces. We complete a theorem begun by G. Chertanov that will establish that for each scadic space X, χ(X) = w(X). A ξ-adic space is a Hausdorff continuous image of a product of compact ordinal spaces. We introduce an either-or chain condition called Property $R_λ^{\prime }$ which we show is satisfied by all ξ-adic spaces. Whereas Property $R_λ^{\prime }$ is productive, we show that a weaker (but more natural) Property $R_λ$ is not productive. Polyadic spaces are shown to satisfy a stronger chain condition called Property $R_λ^{\prime \prime }$. We use Property $R_λ^{\prime }$ to show that not all compact, monolithic, scattered spaces are ξ-adic, thus answering a question of Chertanov’s.

LA - eng

KW - compact; scattered; products; chain condition; ordinals; product of compact scattered spaces; weight; character; dyadic spaces

UR - http://eudml.org/doc/212301

ER -

## References

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