Resovable maps preserve complete metrizability

Su Gao and Vincent Kieftenbeld

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Abstract

Let X be a Polish space, Y a separable metrizable space, and f : X →Y a continuous surjection. We prove that if the image under f of every open set or every closed set is resolvable, then Y is Polish. This generalizes similar results by Sierpinski, Vainstain, and Ostrovsky.

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Table of Contents

1. Introduction

2. Preliminaries

3. Continuous surjections from ω^ω onto Q

4. Main Theorem

           References

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