Isometric embeddings and continuous maps onto the irrationals

2017/06/14 by Elżbieta Pol, Pol, Elżbieta, Roman Pol +1 · 1 citation
Mathematics · #54E40 #54F45 #54H05 #Advanced Topology and Set Theory #FOS: Mathematics #Fixed Point Theorems Analysis #General Topology (math.GN) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1706.04396

openalex publication_date 2017/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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