A note on the prevalent dimensions of continuous images of compact spaces

Details A note on the prevalent dimensions of continuous images of compact spaces A note on the prevalent dimensions of continuous images of compact spaces

2012-03-02

arxiv.org/abs/1203.0548v1

Mathematics

Metric Geometry

Scientific paper

We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. We prove that for a prevalent set of functions in this space, the Hausdorff and packing dimensions of the image is as large as possible, namely 1. We then use this fact to obtain results on the prevalent dimensions of graphs of real-valued continuous functions on compact metric spaces. A particular case complements a result of Bayart and Heurteaux.

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