Article Contents
Article Contents

# An Urysohn-type theorem under a dynamical constraint

• We address the following question raised by M. Entov and L. Polterovich: given a continuous map $f:X\to X$ of a metric space $X$, closed subsets $A,B\subset X$, and an integer $n\geq 1$, when is it possible to find a continuous function $\theta:X\to\mathbb{R}$ such that $\theta f-\theta\leq 1, \quad \theta|A\leq 0, \quad\text{and}\quad \theta|B> n\,?$ To keep things as simple as possible, we solve the problem when $A$ is compact. The non-compact case will be treated in a later work.
Mathematics Subject Classification: Primary: 37B99; Secondary: 37C10.

 Citation:

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