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A dimension raising hereditary shape equivalence

100%

Dijkstra J. J.

Fundamenta Mathematicae

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1996

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tom 149

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nr 3

265-274

EN

We construct a hereditary shape equivalence that raises transfinite inductive dimension from ω to ω+1. This shows that ind and Ind do not admit a geometric characterisation in the spirit of Alexandroff's Essential Mapping Theorem, answering a question asked by R. Pol.

2

Extending monotone mappings

63%

Dijkstra J. J., van Mill J.

Colloquium Mathematicum

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1998

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tom 77

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nr 2

201-210

3

Hausdorff measures and two point set extensions

51%

Dijkstra J. J., Kunen K., van Mill J.

Fundamenta Mathematicae

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1998

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tom 157

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nr 1

43-60

EN

We investigate the following question: under which conditions is a σ-compact partial two point set contained in a two point set? We show that no reasonable measure or capacity (when applied to the set itself) can provide a sufficient condition for a compact partial two point set to be extendable to a two point set. On the other hand, we prove that under Martin's Axiom any σ-compact partial two point set such that its square has Hausdorff 1-measure zero is extendable.

Ograniczanie wyników

2 Fundamenta Mathematicae

1 Colloquium Mathematicum

3 Dijkstra J. J.

2 van Mill J.

1 Kunen K.

2 1998

1 1996

A dimension raising hereditary shape equivalence

Extending monotone mappings

Hausdorff measures and two point set extensions