A Ramsey theorem for polyadic spaces

• Autorzy: Murray G. Bell
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

polyadic; regular closed; uniform Eberlein; hyperspace

Kategorie tematyczne

• 54C35: Function spaces
• 54D30: Compactness
• 54B20: Hyperspaces
• 54B15: Quotient spaces, decompositions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1996
• Tom: 150
• Numer: 2
• Strony: 189-195

Daty

wydano

1996

otrzymano

1995-12-12

poprawiono

1996-01-09

Twórcy

autor

Murray G. Bell

• Department of Mathematics, University of Manitoba, Fort Garry Campus, Winnipeg, Canada R3T 2N2

Bibliografia

• [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.
• [Ge78] J. Gerlits, On a generalization of dyadicity, Studia Sci. Math. Hungar. 13 (1978), 1-17.
• [Mr70] S. Mrówka, Mazur theorem and $\hbox\sgoth m$-adic spaces, Bull. Acad. Polon. Sci. 18 (6) (1970), 299-305.
• [Sh76] L. Shapiro, On spaces of closed subsets of bicompacts, Soviet Math. Dokl. 17 (1976), 1567-1571.