Spaces of piecewise-continuous almost-periodic functions and of almost-periodic sets on the line. I

In connection with the study of piecewise-continuous almost-periodic functions we introduce the notion of a countable almost-periodic number set. We investigate various properties of it: In particular, we prove that the space of almost-periodic sets is closed with respect to the operation of free union.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1613–1619, December, 1991.