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1

A Ramsey theorem for polyadic spaces

100%

Bell M. G.

Fundamenta Mathematicae

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1996

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tom 150

|

nr 2

189-195

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.

2

On character and chain conditions in images of products

100%

Bell M. G.

Fundamenta Mathematicae

|

1998

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tom 158

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nr 1

41-49

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.

3

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A first countable supercompact Hausdorff space with a closed $G_δ$ nonsupercompact subspace

63%

Bell M. G.

Colloquium Mathematicum

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1980

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tom 43

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nr 2

233-241

4

The compactness number of a compact topological space I

45%

Bell M. G., van Mill J.

Fundamenta Mathematicae

|

1980

|

tom 106

|

nr 3

163-173

5

Generalized dyadic spaces

32%

Bell M. G.

Fundamenta Mathematicae

|

1985

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tom 125

|

nr 1

47-58

6

On the combinatorial principle P(c)

32%

Bell M. G.

Fundamenta Mathematicae

|

1981

|

tom 114

|

nr 2

149-157

Ograniczanie wyników

5 Fundamenta Mathematicae

1 Colloquium Mathematicum

6 Bell M. G.

1 van Mill J.

1 1998

1 1996

1 1985

1 1981

2 1980

A Ramsey theorem for polyadic spaces

On character and chain conditions in images of products

A first countable supercompact Hausdorff space with a closed $G_δ$ nonsupercompact subspace

The compactness number of a compact topological space I

Generalized dyadic spaces

On the combinatorial principle P(c)