# Almost periodic sequences and functions with given values

## Michal Veselý

Address: Department of Mathematics and Statistics, Masaryk University, Kotlářská 2, CZ-611 37 Brno, Czech Republic

E-mail: michal.vesely@mail.muni.cz

Abstract: We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set $X$ in a metric space, it is proved the existence of an almost periodic sequence $\lbrace \psi _k\rbrace _{k \in \mathbb{Z}}$ such that $\lbrace \psi _k; \, k \in \mathbb{Z}\rbrace = X$ and $\psi _k = \psi _{k + l q(k)}$, $l \in \mathbb{Z}$ for all $k$ and some $q(k) \in \mathbb{N}$ which depends on $k$.

AMSclassification: primary 11K70; secondary 42A75.

Keywords: almost periodic functions, almost periodic sequences, almost periodicity in metric spaces.