Values of limit periodic sequences and functions (Q2811014)

In the manuscript under consideration the authors consider limit periodic sequences and functions with values in pseudometric spaces. The authors construct limit periodic sequences and functions with given values. For any totally bounded countable set, the authors 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 also proved by the authors. For any totally bounded countable set which is dense in itself, the authors construct a limit periodic bijective map from the integers into this set. As corollaries, the authors obtain new results about non-almost periodic solutions of almost periodic transformable difference systems.NEWLINENEWLINEThe manuscript is very well-written. All the results are clearly stated and their proofs are also given in a lucid manner.