Values of limit periodic sequences and functions

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Authors

VESELÝ Michal HASIL Petr

Year of publication 2016
Type Article in Periodical
Magazine / Source Mathematica Slovaca
MU Faculty or unit

Faculty of Science

Citation
Doi http://dx.doi.org/10.1515/ms-2015-0114
Field General mathematics
Keywords limit periodic sequences; limit periodic functions; almost periodicity; asymptotic almost periodicity
Description We consider limit periodic sequences and functions with values in pseudometric spaces. We construct limit periodic sequences and functions with given values. For any totally bounded countable set, we find a limit periodic sequence which attains each value from this set periodically. A corresponding result concerning such a construction of limit periodic functions is proved as well. For any totally bounded countable set which is dense in itself, we construct a limit periodic bijective map from the integers into this set. As corollaries, we obtain new results about non-almost periodic solutions of almost periodic transformable difference systems.
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