Abstract
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.
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A. Halanay and D. Wexler, The Qualitative Theory of Systems with Impulse [Russian translation], Mir, Moscow (1971).
A. M. Samoilenko, N. A. Perestyuk, and M. U. Akhmetov, Almost-Periodic Solutions of Differential Equations with Impulse Action [in Russian], Preprint No. 83.26, Inst. Mat. Akad. Nauk Ukr. SSR, Kiev (1983).
A. M. Samoilenko and N. A. Perestyuk, Differential Equations with Impulse Action [in Russian], Vishcha Shkola, Kiev (1987).
M. U. Akhmetov and N. A. Perestyuk, “Almost-periodic solutions of nonlinear systems with impulse,” Ukr. Mat. Zh.,41, No. 3, 291–296 (1989).
M. U. Akhmetov, “Recurrent and almost-periodic solutions of nonautonomous systems with impulse,” Izv. Akad. Nauk Kaz. SSR, Fiz.-Mat., No. 3, 8–10 (1988).
A. M. Fink, Almost-Periodic Differential Equations, Lect. Notes on Math., Vol. 337, Springer-Verlag, Berlin-New York (1974).
K. S. Sibirskii, Introduction to Topological Dynamics [in Russian], Redaktsionno-Izd. Otd. Akad. Nauk MSSR, Kishinev (1970).
A. M. Samoilenko and S. I. Trofimchuk, “Unbounded functions with almost-periodic differences,” Ukr. Mat. Zh.,43, No. 10, 1409–1413 (1991).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1613–1619, December, 1991.
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Samoilenko, A.M., Trofimchuk, S.I. Spaces of piecewise-continuous almost-periodic functions and of almost-periodic sets on the line. I. Ukr Math J 43, 1501–1506 (1991). https://doi.org/10.1007/BF01066688
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DOI: https://doi.org/10.1007/BF01066688