# A Ramsey theorem for polyadic spaces

Fundamenta Mathematicae (1996)

- Volume: 150, Issue: 2, page 189-195
- ISSN: 0016-2736

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topBell, Murray. "A Ramsey theorem for polyadic spaces." Fundamenta Mathematicae 150.2 (1996): 189-195. <http://eudml.org/doc/212169>.

@article{Bell1996,

abstract = {A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that $(ακ)^ω$ is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin and M. Wage. Another consequence is that the property of being polyadic is not a regular closed hereditary property.},

author = {Bell, Murray},

journal = {Fundamenta Mathematicae},

keywords = {polyadic; regular closed; uniform Eberlein; hyperspace; polyadic space; uniform Eberlein compact spaces; regular closed hereditary property},

language = {eng},

number = {2},

pages = {189-195},

title = {A Ramsey theorem for polyadic spaces},

url = {http://eudml.org/doc/212169},

volume = {150},

year = {1996},

}

TY - JOUR

AU - Bell, Murray

TI - A Ramsey theorem for polyadic spaces

JO - Fundamenta Mathematicae

PY - 1996

VL - 150

IS - 2

SP - 189

EP - 195

AB - A polyadic space is a Hausdorff continuous image of some power of the one-point compactification of a discrete space. We prove a Ramsey-like property for polyadic spaces which for Boolean spaces can be stated as follows: every uncountable clopen collection contains an uncountable subcollection which is either linked or disjoint. One corollary is that $(ακ)^ω$ is not a universal preimage for uniform Eberlein compact spaces of weight at most κ, thus answering a question of Y. Benyamini, M. Rudin and M. Wage. Another consequence is that the property of being polyadic is not a regular closed hereditary property.

LA - eng

KW - polyadic; regular closed; uniform Eberlein; hyperspace; polyadic space; uniform Eberlein compact spaces; regular closed hereditary property

UR - http://eudml.org/doc/212169

ER -

## References

top- [BRW77] Y. Benyamini, M. E. Rudin and M. Wage, Continuous images of weakly compact subsets of Banach spaces, Pacific J. Math. 70 (1977), 309-324. Zbl0374.46011
- [Ge78] J. Gerlits, On a generalization of dyadicity, Studia Sci. Math. Hungar. 13 (1978), 1-17. Zbl0475.54012
- [Mr70] S. Mrówka, Mazur theorem and $m$-adic spaces, Bull. Acad. Polon. Sci. 18 (6) (1970), 299-305. Zbl0194.54302
- [Sh76] L. Shapiro, On spaces of closed subsets of bicompacts, Soviet Math. Dokl. 17 (1976), 1567-1571. Zbl0364.54013

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