initial value problem; functional differential system; $R_\delta$-set; Kubáček’s theorem; Fréchet space
It is proved that under some conditions the set of solutions to initial value problem for second order functional differential system on an unbounded interval is a compact $R_\delta $-set and hence nonvoid, compact and connected set in a Fréchet space. The proof is based on a Kubáček’s theorem.
 Dugundji, J., Granas, A.: Fixed point theory
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 Kubáček, Z.: Remarks on the paper of K. Czarnowski and T. Pruszko “On the structure of fixed point sets...". Preprint.