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The Dugundji extension property can fail in ωµ -metrizable spaces

100%

Stares I. S., Vaughan J. E.

Fundamenta Mathematicae

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1996

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tom 150

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nr 1

11-16

EN

We show that there exist $ω_μ$-metrizable spaces which do not have the Dugundji extension property ($2^{ω_1}$ with the countable box topology is such a space). This answers a question posed by the second author in 1972, and shows that certain results of van Douwen and Borges are false.

2

Almost disjoint families and property (a)

100%

Szeptycki P. J., Vaughan J. E.

Fundamenta Mathematicae

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1998

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tom 158

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nr 3

229-240

EN

We consider the question: when does a Ψ-space satisfy property (a)? We show that if $|A| < \got p$ then the Ψ-space Ψ(A) satisfies property (a), but in some Cohen models the negation of CH holds and every uncountable Ψ-space fails to satisfy property (a). We also show that in a model of Fleissner and Miller there exists a Ψ-space of cardinality $\got p$ which has property (a). We extend a theorem of Matveev relating the existence of certain closed discrete subsets with the failure of property (a).

3

The smallest number of free closed filters

70%

Pelant J., Simon P., Vaughan J. E.

Fundamenta Mathematicae

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1988

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tom 131

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nr 3

215-221

Ograniczanie wyników

3 Fundamenta Mathematicae

3 Vaughan J. E.

1 Pelant J.

1 Simon P.

1 Stares I. S.

1 Szeptycki P. J.

1 1998

1 1996

1 1988

The Dugundji extension property can fail in ωµ -metrizable spaces

Almost disjoint families and property (a)

The smallest number of free closed filters