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Fundamenta Mathematicae

1998 | 158 | 1 | 41-49
Tytuł artykułu

On character and chain conditions in images of products

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $R_λ'$ which we show is satisfied by all ξ-adic spaces. Whereas Property $R_λ'$ 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 $R_λ''$. We use Property $R_λ'$ to show that not all compact, monolithic, scattered spaces are ξ-adic, thus answering a question of Chertanov's.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
41-49
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-07-29
poprawiono
1998-02-17
Twórcy
autor
• Department of Mathematics, University of Manitoba, Fort Garry Campus, Winnipeg, Manitoba, Canada R3T 2N2, mbell@cc.umanitoba.ca
Bibliografia
• [Ar76] A. Arhangel'skiĭ [A. Arkhangel'skiĭ], z On some topological spaces that occur in functional analysis, Russian Math. Surveys 31 (1976), no. 5, 14-30.
• [Be96] M. Bell, z A Ramsey theorem for polyadic spaces, Fund. Math. 150 (1996), 189-195.
• [Ch88] G. Chertanov, z Continuous images of products of scattered compact spaces, Siberian Math. J. 29 (1988), no. 6, 1005-1012.
• [EHMR84] P. Erdős, A. Hajnal, A. Máté and R. Rado, z Combinatorial Set Theory: Partition Relations for Cardinals, Stud. Logic Found. Math. 106, North-Holland, 1984.
• [Ge73] J. Gerlits, z On a problem of S. Mrówka, Period. Math. Hungar. 4 (1973), no. 1, 71-79.
• [Ho84] R. Hodel, z Cardinal functions I, in: Handbook of Set-Theoretic Topology, K. Kunen and J. Vaughan (eds.), North-Holland, 1984, 1-61.
• [HBA89] S. Koppelberg, z Handbook of Boolean Algebras, Vol. 1, J. D. Monk and R. Bonnet (eds.), North-Holland, 1989.
• [Mr70] S. Mrówka, z Mazur theorem and $\got m$-adic spaces, Bull. Acad. Polon. Sci. 18 (1970), no. 6, 299-305.
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Bibliografia
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