On Borel mappings and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>σ</mml:mi></mml:math>-ideals generated by closed sets

Pol, Roman; Zakrzewski, Piotr

doi:10.1016/j.aim.2012.05.020

Advances in Mathematics

2012

DOI: 10.1016/j.aim.2012.05.020

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On Borel mappings and σ-ideals generated by closed sets

Roman Pol

Piotr Zakrzewski

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Cited by 11 publications

References 14 publications

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On isometric embeddings and continuous maps onto the irrationals

Pol

2018

Monatsh Math

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Let f : E → F be a continuous map of a complete separable metric space E onto the irrationals. We shall show that if a complete separable metric space M contains isometric copies of every closed relatively discrete set in E, then M contains also an isometric copy of some fiber f −1 (y). We shall show also that if all fibers of f have positive dimension, then the collection of closed zero-dimensional sets in E is non-analytic in the Wijsman hyperspace of E. These results, based on a classical Hurewicz's theorem, refine some results from Pol and Pol (Isr J Math 209:187-197, 2015) and answer a question in Banakh et al. (in: Pearl (ed) Open problems in topology II. Elsevier, Amsterdam, 2007).

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On isometric embeddings and continuous maps onto the irrationals

Pol

2018

Monatsh Math

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On Mazurkiewicz’s sets, thin $$\sigma $$-ideals of compact sets and the space of probability measures on the rationals

Pol

Zakrzewski

2021

RACSAM

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On Boolean algebras related to σ-ideals generated by compact sets

Pol

Zakrzewski

2016

Advances in Mathematics

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On Borel mappings and σ-ideals generated by closed sets

Cited by 11 publications

References 14 publications

On isometric embeddings and continuous maps onto the irrationals

On isometric embeddings and continuous maps onto the irrationals

On Mazurkiewicz’s sets, thin $$\sigma $$-ideals of compact sets and the space of probability measures on the rationals

On Boolean algebras related to σ-ideals generated by compact sets

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