Isometric embeddings and continuous maps onto the irrationals

Elżbieta Pol; Roman Pol

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arXiv · 1706.04396

Isometric embeddings and continuous maps onto the irrationals

Elżbieta Pol·Roman Pol

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Abstract

Let f be a continuous map of a complete separable metric space E onto the irrationals. We 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 of f. 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.

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Elżbieta Pol, Roman Pol. 2017-06-14. Isometric embeddings and continuous maps onto the irrationals. https://arxiv.org/abs/1706.04396

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